The document discusses numerical software and tools from NAG for the actuarial community. It provides an overview of NAG, including the types of numerical libraries and toolboxes it offers. It also discusses why numerical computation is important and challenging, and how software providers rely on libraries like NAG rather than writing all numerical code themselves. Actuarial problems that can benefit from NAG libraries are also highlighted.
ISC Frankfurt 2015: Good, bad and ugly of accelerators and a complementary pathJohn Holden
Accelerators Vs Adjoint Algorithmic Differentation (AAD).... NONSENSE. It is not a choice. The two can be combined to provide the ultimate accelerator. Accelerators such as NVIDIA GPUs, Intel Xeon Phis CAN be combined with AD. NAG has the software tools and expertise to deliver AD solutions for traditional architectures and accelerarors
This CFO couldnt understand why a simple spreadsheet with 4 links perpetually broke the reporting cycle - one slide shows what he knew, the second shows the depth of the problem
Numerical Excellence In Finance N A G Jan2010John Holden
The presentation will include examples relevant to finance. Attendees will gain an understanding of how NAG’s mathematical and statistical software can be integrated into many different programs and environments, including Excel, MATLAB (using the NAG Toolbox for MATLAB®), C, C++, and C#.
La gestion de projet dans l'industrie 4.0PMI-Montréal
La gestion de projet dans l’Industrie 4.0
La conférence portera sur la gestion de projet dans l’aire technologique de l’industrie 4.0. La révolution de la collecte de données, de l’analyse de ces données et partage de ces données apporte de nouveaux défis pour les gestionnaires de projets. Que ce soit avant, pendant ou après le projet : les innovations technologiques sont une considération importante pour la livraison des projets du futur.
This document discusses 10 emerging data analytics trends and 5 cooling trends based on an analysis of current technologies and strategies. Emerging trends include self-service BI tools, mobile dashboards, deep learning frameworks like TensorFlow and MXNet, and cloud storage and analysis. Cooling trends include Hadoop due to complexity, batch processing due to lag, and IoT due to security issues. R, Scikit-learn and Jupyter Notebooks are also highlighted as growing in importance.
2.DATAMANAGEMENT-DIGITAL TRANSFORMATION AND STRATEGYGeorgeDiamandis11
The document discusses digitalization in logistics and analytics of key performance indicators. It covers several topics related to data management, including business intelligence, data warehousing, big data, and analytics tools. Case studies are provided on how various organizations have optimized operations, increased speed, and created new services using big data analytics techniques. Examples include detecting fraud, anticipating demand, optimizing inventory, scenario simulation, improving health outcomes, and customizing education.
Qualcomm Webinar: Solving Unsolvable Combinatorial Problems with AIQualcomm Research
How do you find the best solution when faced with many choices? Combinatorial optimization is a field of mathematics that seeks to find the most optimal solutions for complex problems involving multiple variables. There are numerous business verticals that can benefit from combinatorial optimization, whether transport, supply chain, or the mobile industry.
More recently, we’ve seen gains from AI for combinatorial optimization, leading to scalability of the method, as well as significant reductions in cost. This method replaces the manual tuning of traditional heuristic approaches with an AI agent that provides a fast metric estimation.
In this presentation you will find out:
Why AI is crucial in combinatorial optimization
How it can be applied to two use cases: improving chip design and hardware-specific compilers
The state-of-the-art results achieved by Qualcomm AI Research
WSO2 Machine Learner takes data one step further, pairing data gathering and analytics with predictive intelligence: this helps you understand not just the present, but to predict scenarios and generate solutions for the future.
ISC Frankfurt 2015: Good, bad and ugly of accelerators and a complementary pathJohn Holden
Accelerators Vs Adjoint Algorithmic Differentation (AAD).... NONSENSE. It is not a choice. The two can be combined to provide the ultimate accelerator. Accelerators such as NVIDIA GPUs, Intel Xeon Phis CAN be combined with AD. NAG has the software tools and expertise to deliver AD solutions for traditional architectures and accelerarors
This CFO couldnt understand why a simple spreadsheet with 4 links perpetually broke the reporting cycle - one slide shows what he knew, the second shows the depth of the problem
Numerical Excellence In Finance N A G Jan2010John Holden
The presentation will include examples relevant to finance. Attendees will gain an understanding of how NAG’s mathematical and statistical software can be integrated into many different programs and environments, including Excel, MATLAB (using the NAG Toolbox for MATLAB®), C, C++, and C#.
La gestion de projet dans l'industrie 4.0PMI-Montréal
La gestion de projet dans l’Industrie 4.0
La conférence portera sur la gestion de projet dans l’aire technologique de l’industrie 4.0. La révolution de la collecte de données, de l’analyse de ces données et partage de ces données apporte de nouveaux défis pour les gestionnaires de projets. Que ce soit avant, pendant ou après le projet : les innovations technologiques sont une considération importante pour la livraison des projets du futur.
This document discusses 10 emerging data analytics trends and 5 cooling trends based on an analysis of current technologies and strategies. Emerging trends include self-service BI tools, mobile dashboards, deep learning frameworks like TensorFlow and MXNet, and cloud storage and analysis. Cooling trends include Hadoop due to complexity, batch processing due to lag, and IoT due to security issues. R, Scikit-learn and Jupyter Notebooks are also highlighted as growing in importance.
2.DATAMANAGEMENT-DIGITAL TRANSFORMATION AND STRATEGYGeorgeDiamandis11
The document discusses digitalization in logistics and analytics of key performance indicators. It covers several topics related to data management, including business intelligence, data warehousing, big data, and analytics tools. Case studies are provided on how various organizations have optimized operations, increased speed, and created new services using big data analytics techniques. Examples include detecting fraud, anticipating demand, optimizing inventory, scenario simulation, improving health outcomes, and customizing education.
Qualcomm Webinar: Solving Unsolvable Combinatorial Problems with AIQualcomm Research
How do you find the best solution when faced with many choices? Combinatorial optimization is a field of mathematics that seeks to find the most optimal solutions for complex problems involving multiple variables. There are numerous business verticals that can benefit from combinatorial optimization, whether transport, supply chain, or the mobile industry.
More recently, we’ve seen gains from AI for combinatorial optimization, leading to scalability of the method, as well as significant reductions in cost. This method replaces the manual tuning of traditional heuristic approaches with an AI agent that provides a fast metric estimation.
In this presentation you will find out:
Why AI is crucial in combinatorial optimization
How it can be applied to two use cases: improving chip design and hardware-specific compilers
The state-of-the-art results achieved by Qualcomm AI Research
WSO2 Machine Learner takes data one step further, pairing data gathering and analytics with predictive intelligence: this helps you understand not just the present, but to predict scenarios and generate solutions for the future.
This document discusses challenges in developing computer vision software. It explores how the wrong programming model can fail, such as assuming images fit in memory or that pixels can be represented with 8-bit values. Numerical issues are also discussed, like how floating point arithmetic lacks precision. Examples show how simple operations like image differencing, convolution, and calculating standard deviation can have hidden problems. Overall, the document advocates being suspicious of software results and addresses common issues that can cause vision algorithms to go wrong.
Digital Transformation and Process Optimization in ManufacturingBigML, Inc
Keyanoush Razavidinani, Digital Services Consultant at A1 Digital, a BigML Partner, highlights why it is important to identify and reduce human bottlenecks that optimize processes and let you focus on important activities. Additionally, Guillem Vidal, Machine Learning Engineer at BigML completes the session by showcasing how Machine Learning is put to use in the manufacturing industry with a use case to detect factory failures.
IBM hosted its annual IBM Insights On Demand conference to discuss big data analytics trends. The conference highlighted how streaming analytics is becoming more common in enterprises for real-time insights, how financial companies are using sensors and cloud-based solutions innovatively to address big data problems, and how data lakes allow organizations to analyze both structured and unstructured data at rest or in motion. Insurance companies are also using telematics and smart sensors in vehicles to better process claims data and reduce processing times from 2.5 days to just 1.3 days.
Artificial Intelligence in practice - Gerbert Kaandorp - Codemotion Amsterdam...Codemotion
In this talk Gerbert will give an overview of Artificial Intelligence, outline the current state of the art in research and explain what it takes to actually do an AI project. Using practical cases and tools he will give you insight in the phases of an AI project and explain some of the problems you might encounter along the way and how you might be able to solve them.
Bhadale group of companies technology ecosystem for productsVijayananda Mohire
This is our technology stack and ecosystem for our product offerings in various domains. Most of these aid in making best use of emerging technologies and open source
Overview of Watson Cognitive Reservoir Analytics, highlighting how cognitive technologies are ready to address the challenges of the Oil & Gas industry and to transform practices in the industry, in face of data overload, new frontiers, workforce and skills shortage. -Renato Cerqueira, Sr. Research Manager and Technical Team, IBM Research Brazil
Meetup 21/9/2017 - Image Recogonition: onmisbaar voor een slimme stad?Digipolis Antwerpen
1) Image recognition and computer vision technologies can enable various smart city applications like crowd behavior analysis, traffic analysis, and thermal signature tracking.
2) Autonomous systems that use computer vision and machine learning can perceive their environment and act independently to help during disasters by providing survivors and emergency personnel with locating information.
3) MATLAB provides tools for computer vision, machine learning, and deep learning that can help develop prototypes and applications for smart cities from idea to product.
Bhadale group of companies data center products catalogueVijayananda Mohire
This is our first draft version of the product offering in areas of nano computing, DNA computing, Nano wireless network and nano communication. We offer industry standard base images of the solutions for emerging computing platforms and edge, fog computing
Today's bi and data mining ecosystem v2Josep Arroyo
Visualization tools provide predefined reports and dashboards based on a data model to distribute to users, allowing flexible visualization of data through tools like sales per region. Visual Data Mining analyzes raw data to obtain immediate insights through intuitive techniques like customer churn prediction. Data Mining develops accurate predictive models for issues like fraud and risks that are managed by expert statisticians using algorithms and data engineering.
2023 GEOINT Tutorial - Synthetic Data Tools for Computer Vision-Based AI - Re...Chris Andrews
The acquisition of labeled, unbiased, high quality remote sensing information for training AI systems is expensive, error prone, and sometimes impossible or dangerous. The efficacy of Remote Sensing and Imagery Analysis tools that use AI depends directly on the data used for training and validation, meaning that the cost and availability of data limits the application of AI for imagery exploitation. Synthetic Computer Vision (CV) data has become a strategy to reduce the cost and limitations of using real-world data in detection problems in data sparse domains. Focusing on remote sensing data including visible and invisible electromagnetic spectra, attendees will learn about the expanding options for generating synthetic data that are being used in commercial and academic domains, the technology options available for users who want to create CV content of a variety of types, and patterns of creating synthetic data to support
Learning Objectives
- Describe synthetic data including different types such as Generative AI and physics-based data
- Identify the opportunities for applying synthetic data in place of real sensor data
Will be able to describe the steps required to generate synthetic data for computer vision workflows from concept to production for training and validating AI.
- The intent of this class is to introduce the concepts and mechanisms behind the creation of synthetic data and to expose students to approaches for generating synthetic data using tools currently on the market.
- Familiarity with concepts around AI training and validation using remotely sensed data will be helpful for attendees.
RA - Empower your Connected Enterprise with FactoryTalk.pptxAjay Gangakhedkar
The document discusses FactoryTalk InnovationSuite, an IIoT platform powered by PTC that provides data analytics, edge computing, AI, and augmented reality capabilities for empowering the connected enterprise. It presents an overview of the FactoryTalk InnovationSuite and its key components including the ThingWorx IIoT platform, fit for purpose applications, and data analytics tools. The platform allows for mobile/desktop access, orchestration of data sources from traditional and edge systems, and engages users through manufacturing apps, augmented reality, and scalable analytics.
Revolution Analytics provides an advanced analytics platform called Revolution R Enterprise that allows users to leverage the open source R language for big data analytics. The presentation discusses how R can be used to extract value from large, complex datasets through data exploration, visualization, and predictive modeling. It also outlines best practices for implementing an advanced analytics stack and how Revolution R Enterprise optimizes R for distributed computing across multiple data platforms like Hadoop and databases. The key benefits of the Revolution R platform are that it makes R scalable for big data, provides an enterprise-ready environment, and allows organizations to leverage R's flexibility for analytics innovation.
This document contains a presentation by National Instruments that discusses:
1) A warning that projections made in the presentation may differ from actual results.
2) An overview of National Instruments' business including their leadership in computer-based measurement and automation, $821 million in revenue in 2008, and operations in over 40 countries.
3) Their strategic plan for dealing with the current economic environment which includes maintaining a strong cash position, focusing on strategic R&D investment, and managing costs prudently.
This is our first version of the key products that have been used to offer services to our clients. We have about 30 tools mostly open source that are being used at our startup to develop minimum viable products
Neo4j GraphDay Seattle- Sept19- graphs are aiNeo4j
This document discusses how graph databases and machine intelligence are closely related. It provides three examples of how graphs can enhance artificial intelligence:
1. Graph-based algorithms like PageRank and pattern matching can power AI systems. Global graph algorithms can analyze large networks while transactional algorithms can match patterns in graphs.
2. Graphs can assist machine learning by providing features for models. Graph queries can extract smarter features from connected data for ML algorithms. Knowledge graphs also organize information for machine intelligence.
3. Machine intelligence systems can be made more intelligent through the use of graphs. Conversational commerce agents can be built using knowledge graphs to power natural language interactions. Graphs can also provide rich context, enhance AI models,
Beyond Linear Scaling: A New Path for Performance with ScyllaDBScyllaDB
Linear scaling (sometimes near linear scaling) is often mentioned in several benchmarks, articles and product comparisons as proof that a given technology and algorithmic optimizations perform better than another. But is that really what performance is all about, and should you even care?
This webinar discusses performance beyond linear scalability, including what typically matters more when running high throughput and low latency workloads at scale. We'll cover how ScyllaDB offers unparalleled performance and share our insights on:
- The hidden aspects of linear scaling
- When linear scaling matters most and when it’s simply irrelevant
- Often overlooked considerations for optimizing and measuring distributed systems performance
Watch now to learn from our experience (and lessons learned) in building the fastest NoSQL database in the world.
Accelerating algorithmic and hardware advancements for power efficient on-dev...Qualcomm Research
Artificial Intelligence (AI), specifically deep learning, is revolutionizing industries, products, and core capabilities by delivering dramatically enhanced experiences. However, the deep neural networks of today are growing quickly in size and use too much memory, compute, and energy. Plus, to make AI truly ubiquitous, it needs to run on the end device within a tight power and thermal budget. One approach to address these issues is Bayesian deep learning. This presentation covers:
• Why AI algorithms and hardware need to be energy efficient
• How Bayesian deep learning is making neural networks more power efficient through model compression and quantization
• How we are doing fundamental research on AI algorithms and hardware to maximize power efficiency
This document provides an overview of testing artificial intelligence applications. It begins with introductions to Kari Kakkonen and Mark Sevalnev, who will be presenting. The agenda then outlines that the presentation will discuss how AI differs from normal software, areas of AI learning to test, and techniques for testing AI. The document provides background on drivers of the AI revolution and examples of AI applications. It explores how AI is different from traditional software development and when AI approaches are superior. It also addresses challenges in AI like biases in data and fragility. The presentation will cover AI-related terms and concepts. It suggests AI testing life cycles and issues like complexity, bias, and lack of transparency. Example techniques discussed are adversarial attacks and
Mathcad is engineering calculation software used by over 250,000 professionals. It allows users to perform calculations, document their work, and share designs efficiently. New features in Mathcad 14 include improved support for multiple languages, enhanced symbolic solving capabilities, differential equation solving, and plotting tools. These enhancements help users be more productive and improve the quality, clarity, and reuse of intellectual property in engineering designs.
More Related Content
Similar to NAG software for the Actuarial Community (Sep. 2012)
This document discusses challenges in developing computer vision software. It explores how the wrong programming model can fail, such as assuming images fit in memory or that pixels can be represented with 8-bit values. Numerical issues are also discussed, like how floating point arithmetic lacks precision. Examples show how simple operations like image differencing, convolution, and calculating standard deviation can have hidden problems. Overall, the document advocates being suspicious of software results and addresses common issues that can cause vision algorithms to go wrong.
Digital Transformation and Process Optimization in ManufacturingBigML, Inc
Keyanoush Razavidinani, Digital Services Consultant at A1 Digital, a BigML Partner, highlights why it is important to identify and reduce human bottlenecks that optimize processes and let you focus on important activities. Additionally, Guillem Vidal, Machine Learning Engineer at BigML completes the session by showcasing how Machine Learning is put to use in the manufacturing industry with a use case to detect factory failures.
IBM hosted its annual IBM Insights On Demand conference to discuss big data analytics trends. The conference highlighted how streaming analytics is becoming more common in enterprises for real-time insights, how financial companies are using sensors and cloud-based solutions innovatively to address big data problems, and how data lakes allow organizations to analyze both structured and unstructured data at rest or in motion. Insurance companies are also using telematics and smart sensors in vehicles to better process claims data and reduce processing times from 2.5 days to just 1.3 days.
Artificial Intelligence in practice - Gerbert Kaandorp - Codemotion Amsterdam...Codemotion
In this talk Gerbert will give an overview of Artificial Intelligence, outline the current state of the art in research and explain what it takes to actually do an AI project. Using practical cases and tools he will give you insight in the phases of an AI project and explain some of the problems you might encounter along the way and how you might be able to solve them.
Bhadale group of companies technology ecosystem for productsVijayananda Mohire
This is our technology stack and ecosystem for our product offerings in various domains. Most of these aid in making best use of emerging technologies and open source
Overview of Watson Cognitive Reservoir Analytics, highlighting how cognitive technologies are ready to address the challenges of the Oil & Gas industry and to transform practices in the industry, in face of data overload, new frontiers, workforce and skills shortage. -Renato Cerqueira, Sr. Research Manager and Technical Team, IBM Research Brazil
Meetup 21/9/2017 - Image Recogonition: onmisbaar voor een slimme stad?Digipolis Antwerpen
1) Image recognition and computer vision technologies can enable various smart city applications like crowd behavior analysis, traffic analysis, and thermal signature tracking.
2) Autonomous systems that use computer vision and machine learning can perceive their environment and act independently to help during disasters by providing survivors and emergency personnel with locating information.
3) MATLAB provides tools for computer vision, machine learning, and deep learning that can help develop prototypes and applications for smart cities from idea to product.
Bhadale group of companies data center products catalogueVijayananda Mohire
This is our first draft version of the product offering in areas of nano computing, DNA computing, Nano wireless network and nano communication. We offer industry standard base images of the solutions for emerging computing platforms and edge, fog computing
Today's bi and data mining ecosystem v2Josep Arroyo
Visualization tools provide predefined reports and dashboards based on a data model to distribute to users, allowing flexible visualization of data through tools like sales per region. Visual Data Mining analyzes raw data to obtain immediate insights through intuitive techniques like customer churn prediction. Data Mining develops accurate predictive models for issues like fraud and risks that are managed by expert statisticians using algorithms and data engineering.
2023 GEOINT Tutorial - Synthetic Data Tools for Computer Vision-Based AI - Re...Chris Andrews
The acquisition of labeled, unbiased, high quality remote sensing information for training AI systems is expensive, error prone, and sometimes impossible or dangerous. The efficacy of Remote Sensing and Imagery Analysis tools that use AI depends directly on the data used for training and validation, meaning that the cost and availability of data limits the application of AI for imagery exploitation. Synthetic Computer Vision (CV) data has become a strategy to reduce the cost and limitations of using real-world data in detection problems in data sparse domains. Focusing on remote sensing data including visible and invisible electromagnetic spectra, attendees will learn about the expanding options for generating synthetic data that are being used in commercial and academic domains, the technology options available for users who want to create CV content of a variety of types, and patterns of creating synthetic data to support
Learning Objectives
- Describe synthetic data including different types such as Generative AI and physics-based data
- Identify the opportunities for applying synthetic data in place of real sensor data
Will be able to describe the steps required to generate synthetic data for computer vision workflows from concept to production for training and validating AI.
- The intent of this class is to introduce the concepts and mechanisms behind the creation of synthetic data and to expose students to approaches for generating synthetic data using tools currently on the market.
- Familiarity with concepts around AI training and validation using remotely sensed data will be helpful for attendees.
RA - Empower your Connected Enterprise with FactoryTalk.pptxAjay Gangakhedkar
The document discusses FactoryTalk InnovationSuite, an IIoT platform powered by PTC that provides data analytics, edge computing, AI, and augmented reality capabilities for empowering the connected enterprise. It presents an overview of the FactoryTalk InnovationSuite and its key components including the ThingWorx IIoT platform, fit for purpose applications, and data analytics tools. The platform allows for mobile/desktop access, orchestration of data sources from traditional and edge systems, and engages users through manufacturing apps, augmented reality, and scalable analytics.
Revolution Analytics provides an advanced analytics platform called Revolution R Enterprise that allows users to leverage the open source R language for big data analytics. The presentation discusses how R can be used to extract value from large, complex datasets through data exploration, visualization, and predictive modeling. It also outlines best practices for implementing an advanced analytics stack and how Revolution R Enterprise optimizes R for distributed computing across multiple data platforms like Hadoop and databases. The key benefits of the Revolution R platform are that it makes R scalable for big data, provides an enterprise-ready environment, and allows organizations to leverage R's flexibility for analytics innovation.
This document contains a presentation by National Instruments that discusses:
1) A warning that projections made in the presentation may differ from actual results.
2) An overview of National Instruments' business including their leadership in computer-based measurement and automation, $821 million in revenue in 2008, and operations in over 40 countries.
3) Their strategic plan for dealing with the current economic environment which includes maintaining a strong cash position, focusing on strategic R&D investment, and managing costs prudently.
This is our first version of the key products that have been used to offer services to our clients. We have about 30 tools mostly open source that are being used at our startup to develop minimum viable products
Neo4j GraphDay Seattle- Sept19- graphs are aiNeo4j
This document discusses how graph databases and machine intelligence are closely related. It provides three examples of how graphs can enhance artificial intelligence:
1. Graph-based algorithms like PageRank and pattern matching can power AI systems. Global graph algorithms can analyze large networks while transactional algorithms can match patterns in graphs.
2. Graphs can assist machine learning by providing features for models. Graph queries can extract smarter features from connected data for ML algorithms. Knowledge graphs also organize information for machine intelligence.
3. Machine intelligence systems can be made more intelligent through the use of graphs. Conversational commerce agents can be built using knowledge graphs to power natural language interactions. Graphs can also provide rich context, enhance AI models,
Beyond Linear Scaling: A New Path for Performance with ScyllaDBScyllaDB
Linear scaling (sometimes near linear scaling) is often mentioned in several benchmarks, articles and product comparisons as proof that a given technology and algorithmic optimizations perform better than another. But is that really what performance is all about, and should you even care?
This webinar discusses performance beyond linear scalability, including what typically matters more when running high throughput and low latency workloads at scale. We'll cover how ScyllaDB offers unparalleled performance and share our insights on:
- The hidden aspects of linear scaling
- When linear scaling matters most and when it’s simply irrelevant
- Often overlooked considerations for optimizing and measuring distributed systems performance
Watch now to learn from our experience (and lessons learned) in building the fastest NoSQL database in the world.
Accelerating algorithmic and hardware advancements for power efficient on-dev...Qualcomm Research
Artificial Intelligence (AI), specifically deep learning, is revolutionizing industries, products, and core capabilities by delivering dramatically enhanced experiences. However, the deep neural networks of today are growing quickly in size and use too much memory, compute, and energy. Plus, to make AI truly ubiquitous, it needs to run on the end device within a tight power and thermal budget. One approach to address these issues is Bayesian deep learning. This presentation covers:
• Why AI algorithms and hardware need to be energy efficient
• How Bayesian deep learning is making neural networks more power efficient through model compression and quantization
• How we are doing fundamental research on AI algorithms and hardware to maximize power efficiency
This document provides an overview of testing artificial intelligence applications. It begins with introductions to Kari Kakkonen and Mark Sevalnev, who will be presenting. The agenda then outlines that the presentation will discuss how AI differs from normal software, areas of AI learning to test, and techniques for testing AI. The document provides background on drivers of the AI revolution and examples of AI applications. It explores how AI is different from traditional software development and when AI approaches are superior. It also addresses challenges in AI like biases in data and fragility. The presentation will cover AI-related terms and concepts. It suggests AI testing life cycles and issues like complexity, bias, and lack of transparency. Example techniques discussed are adversarial attacks and
Mathcad is engineering calculation software used by over 250,000 professionals. It allows users to perform calculations, document their work, and share designs efficiently. New features in Mathcad 14 include improved support for multiple languages, enhanced symbolic solving capabilities, differential equation solving, and plotting tools. These enhancements help users be more productive and improve the quality, clarity, and reuse of intellectual property in engineering designs.
Similar to NAG software for the Actuarial Community (Sep. 2012) (20)
NAG software for the Actuarial Community (Sep. 2012)
1. Numerical software & tools
for the actuarial community
John Holden
Jacques du Toit
11th September 2012
Actuarial Teachers' and Researchers'
Conference
University of Leicester
Experts in numerical algorithms
and HPC services
2. Agenda
NAG Introduction
Software providers to the Insurance Market
Numerical computation – why bother
Problems in numerical computation
NAG’s Numerical Libraries and Toolboxes
Computational problems in Actuarial Science
Numerical Excellence in Finance 2
3. Numerical Algorithms Group - What We Do
NAG provides mathematical and statistical algorithm
libraries widely used in industry and academia
Established in 1970 with offices in Oxford, Manchester,
Chicago, Taipei, Tokyo
Not-for-profit organisation committed to research &
development
Library code written and contributed by some of the
world’s most renowned mathematicians and computer
scientists
NAG’s numerical code is embedded within many vendor
libraries such as AMD and Intel
Many collaborative projects – e.g. CSE Support to the UK’s
largest supercomputer, HECToR
Numerical Excellence in Finance 3
4. Portfolio
Numerical Libraries
Highly flexible for use in many computing languages, programming
environments, hardware platforms and for high performance
computing methods
Connector Products for Excel, MATLAB, .NET, R and Java
Giving users of the spreadsheets and mathematical software packages
access to NAG’s library of highly optimized and often superior
numerical routines
NAG Fortran Compiler and GUI based Windows
Compiler: Fortran Builder
Visualization and graphics software
Build data visualization applications with NAG’s IRIS Explorer
Consultancy services
Numerical Excellence in Finance 4
5. Software providers to the Insurance Market
ACTUARIS ..
AIR Worldwide ..
Algorithmics Microsoft
Aon Benfield The Numerical Algorithms Group
(NAG)
ARC
AXIS
Oracle Financial Services
Barrie & Hibbert
PolySytems
BPS Resolver
RMS
BWise
SAS Institute
ClusterSeven
SunGard
Conducter
Towers Watson
Conning
Trillium Software
…
Ultimate Risk Solutions
…
WySTAR
Numerical Excellence in Finance 5
6. How is this software made?
Do these software providers write all their own
code?
Do these software providers write all their own
Numerical Code?
Why not?
Numerical Excellence in Finance 6
7. How is this software made?
Do these software providers write all their own
code?
No
Do these software providers write all their own
Numerical Code?
No
Why not?
Let’s take a look
Numerical Excellence in Finance 7
8. Why bother?
Numerical computation is difficult to do
accurately
Problems of
Overflow / underflow
How does the computation behave for large / small numbers?
Condition
How is it affected by small changes in the input?
Stability
How sensitive is the computation to rounding errors?
Importance of
error analysis
information about error bounds on solution
Numerical Excellence in Finance 8
9. An example: sample variance
For a collection of observations
{xi ,,ii 1...n}
{xi 1...n}
the mean is defined as
1 n
x xi
n i 1
and the variance as
n
1
s
2
( xi x )
n 1 i 1
2
Numerical Excellence in Finance 9
10. Example calculation
For this collection of observations
{c 1, c, c 1}
the mean is
x 1 (c 1 c c 1) c
3
and the variance is
s
2 1 (( 1)2 0 12 ) 1
2
<Excel – variance demo>
Numerical Excellence in Finance 10
11.
12.
13.
14.
15. What’s gone wrong?
Instead of
1 n
s
2
( xi x )
n 1 i 1
2
Excel uses an (analytically identical) formula
1 n 1 n
2
s
2
xi xi
2
n 1 i1 n i1
(one pass)
faster to calculate
accuracy problems if variance is small compared to x
Numerical Excellence in Finance 15
16. Software providers to the Insurance Market
ACTUARIS ..
AIR Worldwide ..
Algorithmics Microsoft
Aon Benfield The Numerical Algorithms Group
(NAG)
ARC
AXIS
Oracle Financial Services
Barrie & Hibbert
PolySytems
BPS Resolver
RMS
BWise
SAS Institute
ClusterSeven
SunGard
Conducter
Towers Watson
Conning
Trillium Software
…
Ultimate Risk Solutions
…
WySTAR
Numerical Excellence in Finance 16
17. Numerical computation – DIY Vs NAG
DIY implementations of numerical components have
their place, but NOT in production code.
Handwritten and “hand me down” type code might be
easy to implement, but will…
NOT be well tested
NOT fast
NOT stable
NOT deliver good error handling
NAG implementations in contrast are fast and
Accurate
Well tested
Thoroughly documented
Give “qualified error” messages e.g. tolerances of answers (which
the user can choose to ignore, but avoids proceeding blindly)
Numerical Excellence in Finance 17
18. Why People use NAG Libraries and Toolboxes?
Global reputation for quality – accuracy, reliability
and robustness…
Extensively tested, supported and maintained code
Reduces development time
Allows concentration on your key areas
Components
Fit into your environment
Simple interfaces to your favourite packages
Regular performance improvements!
Numerical Excellence in Finance 18
19. NAG provides the atomic bricks
… for the domain specialists to build the walls,
houses and fancy castles!
Users know NAG Components are here today,
tomorrow and beyond
Functions are not removed when new ones added without
sensible notice and advice
NAG functions are well documented
Lets take a look….
Numerical Excellence in Finance 19
20. NAG Library and Toolbox Contents
Root Finding Dense Linear Algebra
Summation of Series Sparse Linear Algebra
Quadrature Correlation & Regression
Ordinary Differential Analysis
Equations Multivariate Methods
Partial Differential Equations Analysis of Variance
Numerical Differentiation Random Number Generators
Integral Equations Univariate Estimation
Mesh Generation Nonparametric Statistics
Interpolation Smoothing in Statistics
Curve and Surface Fitting Contingency Table Analysis
Optimization Survival Analysis
Approximations of Special Time Series Analysis
Functions Operations Research
Numerical Excellence in Finance 20
21. NAG Data Mining Components
Data Cleaning Regression
Data Imputation Regression Trees
Outlier Detection
Linear Regression
Multi-layer Perceptron Neural
Data Transformations Networks
Scaling Data
Principal Component Analysis Nearest Neighbours
Radial Basis Function Models
Cluster Analysis Association Rules
k-means Clustering Utility Functions
Hierarchical Clustering
To support the main functions
and help with prototyping
Classification
Classification Trees
Generalised Linear Models
Nearest Neighbours
Numerical Excellence in Finance 21
22. NAG routines for GPUs
Random Number Generators
L’Ecuyer mrg32k3a and Mersenne Twister (with skip-
ahead) mt19937
Uniform distribution
Normal distribution
Exponential distribution
Support for multiple streams and sub-streams
Sobol sequence for Quasi-Monte Carlo ( up to 50,000
dimensions)
Scrambled sequencing for Sobol (Hickernell)
Brownian Bridge
Numerical Excellence in Finance 22
23. Traditional Uses of NAG Libraries
NAG is used where non-trivial mathematics must be
done quickly and accurately on computers
Largest user groups (not in order)
Academic researchers (typically Statistics, Applied
Mathematics, Finance, Economics, Physics, Engineering)
Engineers (fluid dynamics, large-scale PDE problems,
simulations)
Statisticians (data mining, model fitting, analysis of
residuals, time series, … )
Quantitative analysts (asset modelling and risk analysis)
Numerical Excellence in Finance 23
24. Use of NAG Software in Statistics
Multivariate Methods (G02/G04)
Nearest correlation matrix, generalised regression with
various error distributions (with and without missing data),
robust/ridge/partial least squares regression, mixed effects
and quantile regression, …
Nonparametric Statistics (G08)
Hypothesis testing
Survival Analysis (G12)
Time Series Analysis (G13)
SARIMA, VARMA, GARCH, with various modifications
Random Number Generators (G05)
Numerical Excellence in Finance 24
25. The NAG Library and Actuarial Statistics
Survival models:
Cox regression model (g12bac)
Kaplan-Meier estimator (g12aac)
Weibull, exponential and extreme values (via g01gcc)
Risk analysis/ loss functions:
Distributions:
lognormal, gamma, beta etc both distribution functions (g01) &
random number generation (g05).
Other
Time series (g05 and g13)
Convolutions: FFT's (c06)
Kernel density estimation
Graduation: generalised linear models (g02g)
Analysis of risk factors: generalised linear models (g02g)
Numerical Excellence in Finance 25
26. Use of NAG Software in Finance
Portfolio analysis / Index tracking / Risk management
Optimization , linear algebra, copulas…
Derivative pricing
PDEs, RNGs, multivariate normal, …
Fixed Income/ Asset management / Portfolio
Immunization
Operations research
Data analysis
Time series, GARCH, principal component analysis, data smoothing,
…
Monte Carlo simulation
RNGs
……
Numerical Excellence in Finance 26
27. Why Quantitative Analysts Love NAG?
General Problem
To build asset models and risk engines in a timely manner
that are
Robust
Stable
Quick
Solution
Use robust, well tested, fast numerical components
This allows the “expensive” experts to concentrate on the
modelling and interpretation
avoiding distraction with low level numerical components
Numerical Excellence in Finance 27
28. Problem 1: Simulation (Monte Carlo)
Simulation is important for scenario generation
Several different numerical components needed
Random Number Generators
Brownian bridge constructor
Interpolation/Splines
Principal Component Analysis
Cholesky Decomposition
Distributions (uniform, Normal, exponential gamma,
Poisson, Student’s t, Weibull,..)
..
Numerical Excellence in Finance 28
29. Problem 1: Simulation (Monte Carlo)
Simulation is important for scenario generation
NAG to the rescue (CPU or GPU)
Several different numerical components needed
Random Number Generators √
Brownian bridge constructor √
Interpolation/Splines √
Principal Component Analysis√
Cholesky Decomposition √
Distributions (uniform, Normal, exponential gamma,
Poisson, Student’s t, Weibull,..)√
.. √ √
Numerical Excellence in Finance 29
30. Problem 2: Calibration
Financial institutions all need to calibrate their
models
Several different numerical components needed
Optimisation functions (e.g. constrained non-linear
optimisers)
Interpolation functions
Spline functions
..
Numerical Excellence in Finance 30
31. Problem 2: Calibration
Financial institutions all need to calibrate their
models
NAG to the rescue
Several different numerical components needed
Optimisation functions (e.g. constrained non-linear
optimisers) √
Interpolation functions (used intelligently*) √
Spline functions √
.. √ √
*interpolator must be used carefully –must know the properties to pick appropriate method
Numerical Excellence in Finance 31
32. Problem 3: Historical VaR
VaR methodology (important for identifying what
variables might impact you most (eg Yen Vs USD))
Several different numerical components needed
Time Series
Correlation and Regressions
Matrix functions
Cholesky Decomp
RNGs ..
Numerical Excellence in Finance 32
33. Problem 3: Historical VaR
VaR methodology (important for identifying what
variables might impact you most (eg Yen Vs USD))
NAG to the rescue
Several different numerical components needed
Time Series √
Correlation and Regressions √
Matrix functions √
Cholesky Decomp √
RNGs .. √ √
Numerical Excellence in Finance 33
34. NAG fits into your favourite environments
Supporting Wide Range of Operating systems…
Windows, Linux, Solaris, Mac, …
…and a number of interfaces
C, C++, Excel,
Fortran, LabVIEW,
VB, Excel & VBA, MATLAB,
C#, F#, VB.NET, Maple,
CUDA, OpenCL, Mathematica
Java, R, S-Plus,
Python Scilab, Octave
… …
Numerical Excellence in Finance 34
35. NAG and Excel
Our libraries are easily accessible from Excel:
Calling NAG DLLs using
VBA
NAG provide VB
Declaration Statements
and Examples
NAG provide “Add-ins”
Calling NAG Library for
.NET using VSTO
Functions with Reverse
Communication (useful
for Solver replication for
example) can be
provided
Create NAG XLLs
Numerical Excellence in Finance 35
37. Example – Kaplan-Meier survival probabilities
Data
Life tables for WHO Member States
Global level of child and adult mortality
http://www.who.int/healthinfo/statistics/mortality_life_ta
bles/en/index.html
How many people out 0f 100,000 die at birth, until 1YO,
5YO, etc. and how many people live 100 years or longer
Numerical Excellence in Finance 37
38. Input … and … output …
Numerical Excellence in Finance 38
39. … followed by Excel plot
Numerical Excellence in Finance 39
40. How do you call the functions in Excel
Numerical Excellence in Finance 40
41. How do you call the functions in Excel
Enter the
inputs from the
spreadsheet
Excel function
wizard
Numerical Excellence in Finance 41
42. What’s under the hood?
NAG Library
function called
via VBA
Numerical Excellence in Finance 42
43. NAG and .NET
NAG solutions for .NET
1. Call NAG C (or Fortran) DLL from C#
2. NAG Library for .NET
“a more natural solution”
DLL with C# wrappers
Integrated help
Not yet the full Library, but most widely used chapters
included.
Very popular with .NET dev community inc. in
Financial Services.
Numerical Excellence in Finance 43
44. NAG Toolbox for MATLAB
Contains essentially all NAG functionality
not a subset
Runs under Windows (32/64bit), Linux (32/64-
bit) and Mac (64 bit).
Comprehensive documentation (in MATLAB and
pdf)
Easy migration to production code in C/C++ or
Fortran
Can be used with MATLAB compiler
Numerical Excellence in Finance 44
45. NAG Toolbox help MATLAB formatting NAG formatting
Numerical Excellence in Finance 45
chapters (in PDF)
46. NAG Toolbox for MATLAB
Offers complementary functionality to MATLAB
Alternative to several specialist toolboxes
“I really like the NAG Toolbox for MATLAB for
the following reasons (among others):
It can speed up MATLAB calculations – see my article on MATLAB’s
interp1 function for example.
Their support team is superb.”
http://www.walkingrandomly.com/?p=160
Senior Developer
“concerning the ‘nearest correlation’ algorithm. I have to say, it is
very fast, it uses all the power of my pc and the result is very
satisfactory.”
Numerical Excellence in Finance 46
47. Computational problems in Actuarial Science
Liability Modelling
Asset Modelling
Solvency II
Nearest Correlation Matrix example
Numerical Excellence in Finance 47
48. Liability Modelling
“Traditional” actuarial science is focused
predominantly on liability modelling
Forecast cash flows directly linked to mortality/longevity
Example: a pension scheme. Premiums received until
retirement, pension paid until death, lump sum paid upon
death
Requires some modelling of market conditions
(assumptions on inflation, gilt yields, index returns, … )
Fair to say often this modelling is not very sophisticated
and is not very computationally demanding.
Numerical Excellence in Finance 48
49. Asset Modelling
Liability modelling very well understood
Been doing it for more than two centuries, mostly get it
right (sometimes get it wrong)
Commercial packages to do this (Prophet, MoSes, …)
Often heavily regulated (e.g. pensions)
Asset modelling, in the actuarial context, perhaps
less so
Traditional view been to model average behaviour over
long horizons – simplicity is sensible, since so many
assumptions anyway
Numerical Excellence in Finance 49
50. Solvency II
There is a regulatory push to change this
“Solvency II = Basel for insurers”
Similar risk methodology as banks, being introduced for
insurers
Aim is to stress insurer’s balance sheet to various shocks,
especially market shocks
Requires more explicit modelling of assets
Initial guidelines laid down by regulator – pretty simplistic
However, as with Basel, insurers encouraged to develop
own approaches (which would be less punitive)
Horizons fairly short-dated
Numerical Excellence in Finance 50
51. Solvency II
Asset modelling is difficult!
Ask a financial mathematician (or a quant)
Technically demanding and computationally demanding
Moreover, every market is unique
Not just across asset classes, but different countries as
well. No “one-size-fits-all” approach possible
Each has own behaviour, own peculiarities
NAG Library used extensively for building
sophisticated, robust asset models and risk engines
Numerical Excellence in Finance 51
53. Example: Nearest Correlation Matrix
Mathematically, a correlation matrix 𝐶 ∈ ℝ 𝑛×𝑛 is ...
1. Square
2. Symmetric with ones on diagonal
3. Is positive semi-definite: 𝑥 𝑇 𝐶𝑥 ≥ 0 for all 𝑥 ∈ ℝ 𝑛
How do we estimate correlations?
Historical data
Parametric methods such as Gaussian Copulas
Try to back it out from options markets
Typically 1 and 2 easy enough to ensure
Ensuring positive semi-definite can be tricky
Numerical Excellence in Finance 53
54. Example: Nearest Correlation Matrix
Historical data
Take time series for several observables and try to
estimate correlation
Gaussian copula
Model for turning a set of marginals + a correlation matrix
into a joint distribution.
Was popular in credit modelling until 2008/9 proved it was
(in many cases) wholly inadequate
Infer from options markets
Combine individual options and options on indexes to back
out correlation structure
Numerical Excellence in Finance 54
55. Example: Nearest Correlation Matrix
In all these cases, need to work with correlation
matrices estimated from “real world” data
Real data is messy
Given importance of correlation, what happens if
estimate not mathematically correct?
Numerical Excellence in Finance 55
56. Example: Nearest Correlation Matrix
NAG Library can find the “nearest” correlation matrix
to a given square matrix 𝐴
2
G02AA solves the problem min 𝐶 𝐴 − 𝐶 𝐹 in Frobenius
norm
G02AB incorporates weights min 𝐶 𝑊 1/2 𝐴− 𝐶 𝑊 1/2 2
𝐹
Weights useful when have more confidence in accuracy of
observations for certain observables than for others
Numerical Excellence in Finance 56
57. Example: Nearest Correlation Matrix
The effect of W:
A =
0.4218 0.6557 0.6787 0.6555
0.9157 0.3571 0.7577 0.1712
0.7922 0.8491 0.7431 0.7060
0.9595 0.9340 0.3922 0.0318
W = diag([10,10,1,1])
W*A*W = Whole rows/cols
42.1761 65.5741 6.7874 6.5548 weighted by 𝑤 𝑖
91.5736 35.7123 7.5774 1.7119
7.9221 8.4913 0.7431 0.7060 Elements weighted
9.5949 9.3399 0.3922 0.0318 by 𝑤 𝑖 ∗ 𝑤 𝑗
Numerical Excellence in Finance 57
58. Example: Nearest Correlation Matrix
Can also do dimension reduction (G02AE)
So-called factor models. Similar to PCA in regression
Suppose have assets 𝑌1 , ⋯ , 𝑌 𝑛 , an 𝑛 dimensional source
of noise 𝑊 and an 𝑛 × 𝑛 “correlation” matrix 𝐴 where
Yt1 Wt1
Ft A
Yt n Wt n
For example, a simple multi-asset model: one factor (e.g.
Brownian motion) for each asset, and 𝐴𝐴 𝑇 gives
correlation between all factors
Numerical Excellence in Finance 58
59. 3rd Example: Nearest Correlation Matrix
Can use NAG Library to reduce the number of factors
Find a n × 𝑘 matrix D (where 𝑘 < 𝑛) such that
Yt1 Wt1
Ft D
Yt n Wt k
Crucially, 𝐷𝐷 𝑇 gives a correlation structure as close as
possible to the original structure implied by 𝐴
Can be very useful to reduce complexity and
computational cost of some models and applications
Numerical Excellence in Finance 59
61. NAG is a HPCFinance partner
http://www.hpcfinance.eu
The network is recruiting for
Early Stage Researchers (ESRs ~ PhD Students)
Experienced Researchers (ERs in Post Docs)
Numerical Excellence ~ Finance 61
62. NAG and Actuarial Science - Summary
NAG is keen to collaborate in building actuarial
models and risk engines
Your requirements likely to be different from banks/hedge
funds
We want to make sure we have what you need
Risk engines likely to involve a LOT of computation
NAG has significant experience in HPC services, consulting
and training
We know how to do large scale computations efficiently
This is non-trivial! Our expertise has been sought out and
exploited by organisations such as (BP, HECToR, Microsoft,
Oracle, Rolls Royce, …….)
Numerical Excellence in Finance 62
63. Keep in touch
Many of you are already licensed to use NAG software….
Technical Support and Help
support@nag.co.uk
To reach the speakers
john.holden@nag.co.uk
jacques@nag.co.uk
NAGNews
http://www.nag.co.uk/NAGNews/Index.asp
Numerical Excellence in Finance 63