1) The document analyzes the impact of proportional reinsurance on ruin probabilities in an insurance surplus process compounded with interest.
2) A model is presented where the insurance surplus follows a diffusion process and the company invests surplus in risk-free assets while purchasing proportional reinsurance.
3) Results are presented for different claim distributions and levels of proportional reinsurance, interest rates, and initial surplus. Ruin probabilities are estimated numerically.
Christopher Stender is an immigration attorney who is fluent in both Spanish and German. With more than a decade of experience practicing immigration law, he has successfully argued numerous cases on behalf of clients facing deportation before the Board of Immigration Appeals and the 9th Circuit Court of Appeals. In his spare time, Christopher Stender has donated his time or financial support to several charities including Homeless Outreach, Cesar Chavez School Mission, and the Florence Immigrant & Refugee Rights Project (FIRRP).
Yhden päivän Facebook-koulutuksessa käymme läpi Facebookin ominaisuuksia ja opimme keinoja, miten yritykset saavat siitä enemmän irti. Yritykset Facebookissa-koutuksessa saat uusia ideoita Facebookin käyttöön työssäsi: Facebookissa voit viestiä, tiedottaa, markkinoida, seurata uutisia ja oppia uutta. Tutustut Facebookin ominaisuuksiin ja opit tekemään kohderyhmillenne entistä parempaa sisältöä. Koulutus on osallistava ja sisältää paljon käytännön harjoituksia sekä keskusteluja, joiden aikana voit miettiä, miten juuri teidän kannattaa Facebookissa toimia. Käytetyt esimerkit poimitaan suomalaisten yritysten sivuilta ja ryhmistä, jotta niihin on helpompi samaistua.
Christopher Stender is an immigration attorney who is fluent in both Spanish and German. With more than a decade of experience practicing immigration law, he has successfully argued numerous cases on behalf of clients facing deportation before the Board of Immigration Appeals and the 9th Circuit Court of Appeals. In his spare time, Christopher Stender has donated his time or financial support to several charities including Homeless Outreach, Cesar Chavez School Mission, and the Florence Immigrant & Refugee Rights Project (FIRRP).
Yhden päivän Facebook-koulutuksessa käymme läpi Facebookin ominaisuuksia ja opimme keinoja, miten yritykset saavat siitä enemmän irti. Yritykset Facebookissa-koutuksessa saat uusia ideoita Facebookin käyttöön työssäsi: Facebookissa voit viestiä, tiedottaa, markkinoida, seurata uutisia ja oppia uutta. Tutustut Facebookin ominaisuuksiin ja opit tekemään kohderyhmillenne entistä parempaa sisältöä. Koulutus on osallistava ja sisältää paljon käytännön harjoituksia sekä keskusteluja, joiden aikana voit miettiä, miten juuri teidän kannattaa Facebookissa toimia. Käytetyt esimerkit poimitaan suomalaisten yritysten sivuilta ja ryhmistä, jotta niihin on helpompi samaistua.
We study influence maximization in which diffusion on each step may be delayed, and the objective is to maximize influence spread within a certain deadline. Both IC and LT models are extended, and efficient algorithms are proposed and evaluated.
This work appears in AAAI 2012. For the full version of the paper, please see: http://arxiv.org/abs/1204.3074
Presentation by Guillaume Touya at GIScience conference 2012Guillaume Touya
Presentation by Guillaume Touya at GIScience conference 2012 of a method to assess the global legibility of a generalised map based on social welfare techniques.
First presented at the MSUG Conference on June 4, 2015, this presentation discusses concepts and tools to add to your logistic regression modeling practice and also how to use these concepts and tools.
The dangers of policy experiments Initial beliefs under adaptive learningGRAPE
The paper studies the implication of initial beliefs and associated confidence on the system’s
dynamics under adaptive learning. We first illustrate how prior beliefs determine learning dynamics
and the evolution of endogenous variables in a small DSGE model with credit-constrained agents,
in which rational expectations are replaced by constant-gain adaptive learning. We then examine
how discretionary experimenting with new macroeconomic policies is affected by expectations that
agents have in relation to these policies. More specifically, we show that a newly introduced macroprudential policy that aims at making leverage counter-cyclical can lead to substantial increase in
fluctuations under learning, when the economy is hit by financial shocks, if beliefs reflect imperfect
information about the policy experiment. This is in the stark contrast to the effects of such policy
under rational expectations.
Spillover dynamics for systemic risk measurement using spatial financial time...SYRTO Project
Spillover dynamics for systemic risk measurement using spatial financial time series models - Blasques F., Koopman S.J., Lucas A., Schaumburg J. June, 12 2014. 7th Annual SoFiE (Society of Financial Econometrics) Conference
Information Object Model (IOM) is
- first developed at ISP-NICT, Japan
- used for managing spatio-temporal-semantic events detected from heterogeneous sensors
- published in
[1] Minh-Son Dao, Koji Zettsu, Siripen Pongpaichet, Laleh Jalali, Ramesh Jain: Exploring spatio-temporal-theme correlation between physical and social streaming data for event detection and pattern interpretation from heterogeneous sensors. Big Data 2015: 2690-2699
Demo of using IOM in detect events affected by heavy rain in Japan, here
https://www.youtube.com/watch?v=vkvzZuP8W60
OECD EU Expert Meeting on Disaster Loss Data, 26-28 October 2016OECD Governance
This expert meeting was organised jointly by the European Commission, the OECD and the project PLACARD. For more information see www.oecd.org/gov/risk/joint-expert-meeting-on-disaster-loss-data.htm
UTC is well-known for producing multi-facet, wide-ranging engineers. They can be top-notch technically or
skilful managers, or a mix of both – this is largely due to the cursus structure, with its 6 elective majors
and 24 optional specialties that opens the way to innumerable professional opportunities. That is why there
is no stereotype profile for a UTC graduate … This month’s ‘dossier’ looks at this rich diversity and invites
the students to tell us how they perceived their last placement, just before they are invited to their muchawaited
UTC graduation ceremony? The following short stories, in a sense, help the future graduates to project
themselves into a job context. We shall be able to follow their first steps. Twice a year, 1 000 industrial training
officers, UTC’s pedagogical tutors and the trainees meet for the poster session day devoted to the placements.
The students have 15 minutes each to valorise their experience!
Disaster and crisis management is a global problem. Scenarios range from short-term localized events to those with widespread impact persisting for years or decades. From personal experience and research in the topic area, there is clearly a need for a technology “platform” that can integrate cross-disciplinary agencies, civilians, contractors, and any other conceivable stakeholder. These stakeholders (including the environment and the public) will benefit immensely from integration and standardization in a problem-solving environment, especially in light of the value of human life. This approach should lead to enhanced preservation of life and safety, reduced environmental impact, and overall improvement in disaster response and mitigation – irrespective of the disaster type or scale.
Foundations of Statistics for Ecology and Evolution. 4. Maximum LikelihoodAndres Lopez-Sepulcre
1. Maximum Likelihood Estimation
- The abductive method
- How to fit a model to data
2. Calculating parameter Uncertainty
3. Comparing Multiple Hypotheses
- Alternatives beyond rejection
- Parsimony and information
Selection of most economical green building out of n alternatives approach ...eSAT Journals
Abstract
The concept of green building are now very effective tool to an engineer for construction of a new building and plays a vital role to influence his decision towards saving of water & electricity, providing healthier spaces, and generate less quantity of wastes during constructional period[3]. The quality and quantity of materials are directly gives the output efficiency in respect of the economy as well as positive environmental condition of a green building. But it is often found that total cost of building and total environmental impact values (TEIV) (inside and outside) are not same for all buildings constructed in various places due to fluctuation of market rate from place to place[4]. Thus to define a most economical green building out of n-alternatives, total cost of the building and it’s TEIV are very essential factors for assessment and making rank among them. But it is not a easy job because most of the data are not always crisp or numeric rather linguistic and hedges like ‘high reflective roof coating’, ‘bad orientation’, ‘poor sanitation’, ‘very good environmental quality’, ‘cheap materials’, ‘good drainage system’, ‘heavy rainfall’, ‘high energy consumption’, etc. to list a few only out of infinity. All these data are fuzzy in nature thus evaluation of many objects here is not possible with numerical valued descriptions[1]. All experts’ perception towards giving his decision depends wholly on his neural network functions which fluctuate according to the nature of function of dendrite and axon. Thus every decision-maker hesitates more or less on every evaluation activity which needs to be eliminated. The fuzzy logic has now proved worldwide as a tremendous tool to tackle this situation. This paper presents a fuzzy modelling for selection of most economical green building (GB) out of n-alternatives more precisely.
Keywords: attributes, fuzzy decision, TEIV, vague fuzzy EIA, etc.
We study influence maximization in which diffusion on each step may be delayed, and the objective is to maximize influence spread within a certain deadline. Both IC and LT models are extended, and efficient algorithms are proposed and evaluated.
This work appears in AAAI 2012. For the full version of the paper, please see: http://arxiv.org/abs/1204.3074
Presentation by Guillaume Touya at GIScience conference 2012Guillaume Touya
Presentation by Guillaume Touya at GIScience conference 2012 of a method to assess the global legibility of a generalised map based on social welfare techniques.
First presented at the MSUG Conference on June 4, 2015, this presentation discusses concepts and tools to add to your logistic regression modeling practice and also how to use these concepts and tools.
The dangers of policy experiments Initial beliefs under adaptive learningGRAPE
The paper studies the implication of initial beliefs and associated confidence on the system’s
dynamics under adaptive learning. We first illustrate how prior beliefs determine learning dynamics
and the evolution of endogenous variables in a small DSGE model with credit-constrained agents,
in which rational expectations are replaced by constant-gain adaptive learning. We then examine
how discretionary experimenting with new macroeconomic policies is affected by expectations that
agents have in relation to these policies. More specifically, we show that a newly introduced macroprudential policy that aims at making leverage counter-cyclical can lead to substantial increase in
fluctuations under learning, when the economy is hit by financial shocks, if beliefs reflect imperfect
information about the policy experiment. This is in the stark contrast to the effects of such policy
under rational expectations.
Spillover dynamics for systemic risk measurement using spatial financial time...SYRTO Project
Spillover dynamics for systemic risk measurement using spatial financial time series models - Blasques F., Koopman S.J., Lucas A., Schaumburg J. June, 12 2014. 7th Annual SoFiE (Society of Financial Econometrics) Conference
Information Object Model (IOM) is
- first developed at ISP-NICT, Japan
- used for managing spatio-temporal-semantic events detected from heterogeneous sensors
- published in
[1] Minh-Son Dao, Koji Zettsu, Siripen Pongpaichet, Laleh Jalali, Ramesh Jain: Exploring spatio-temporal-theme correlation between physical and social streaming data for event detection and pattern interpretation from heterogeneous sensors. Big Data 2015: 2690-2699
Demo of using IOM in detect events affected by heavy rain in Japan, here
https://www.youtube.com/watch?v=vkvzZuP8W60
OECD EU Expert Meeting on Disaster Loss Data, 26-28 October 2016OECD Governance
This expert meeting was organised jointly by the European Commission, the OECD and the project PLACARD. For more information see www.oecd.org/gov/risk/joint-expert-meeting-on-disaster-loss-data.htm
UTC is well-known for producing multi-facet, wide-ranging engineers. They can be top-notch technically or
skilful managers, or a mix of both – this is largely due to the cursus structure, with its 6 elective majors
and 24 optional specialties that opens the way to innumerable professional opportunities. That is why there
is no stereotype profile for a UTC graduate … This month’s ‘dossier’ looks at this rich diversity and invites
the students to tell us how they perceived their last placement, just before they are invited to their muchawaited
UTC graduation ceremony? The following short stories, in a sense, help the future graduates to project
themselves into a job context. We shall be able to follow their first steps. Twice a year, 1 000 industrial training
officers, UTC’s pedagogical tutors and the trainees meet for the poster session day devoted to the placements.
The students have 15 minutes each to valorise their experience!
Disaster and crisis management is a global problem. Scenarios range from short-term localized events to those with widespread impact persisting for years or decades. From personal experience and research in the topic area, there is clearly a need for a technology “platform” that can integrate cross-disciplinary agencies, civilians, contractors, and any other conceivable stakeholder. These stakeholders (including the environment and the public) will benefit immensely from integration and standardization in a problem-solving environment, especially in light of the value of human life. This approach should lead to enhanced preservation of life and safety, reduced environmental impact, and overall improvement in disaster response and mitigation – irrespective of the disaster type or scale.
Foundations of Statistics for Ecology and Evolution. 4. Maximum LikelihoodAndres Lopez-Sepulcre
1. Maximum Likelihood Estimation
- The abductive method
- How to fit a model to data
2. Calculating parameter Uncertainty
3. Comparing Multiple Hypotheses
- Alternatives beyond rejection
- Parsimony and information
Selection of most economical green building out of n alternatives approach ...eSAT Journals
Abstract
The concept of green building are now very effective tool to an engineer for construction of a new building and plays a vital role to influence his decision towards saving of water & electricity, providing healthier spaces, and generate less quantity of wastes during constructional period[3]. The quality and quantity of materials are directly gives the output efficiency in respect of the economy as well as positive environmental condition of a green building. But it is often found that total cost of building and total environmental impact values (TEIV) (inside and outside) are not same for all buildings constructed in various places due to fluctuation of market rate from place to place[4]. Thus to define a most economical green building out of n-alternatives, total cost of the building and it’s TEIV are very essential factors for assessment and making rank among them. But it is not a easy job because most of the data are not always crisp or numeric rather linguistic and hedges like ‘high reflective roof coating’, ‘bad orientation’, ‘poor sanitation’, ‘very good environmental quality’, ‘cheap materials’, ‘good drainage system’, ‘heavy rainfall’, ‘high energy consumption’, etc. to list a few only out of infinity. All these data are fuzzy in nature thus evaluation of many objects here is not possible with numerical valued descriptions[1]. All experts’ perception towards giving his decision depends wholly on his neural network functions which fluctuate according to the nature of function of dendrite and axon. Thus every decision-maker hesitates more or less on every evaluation activity which needs to be eliminated. The fuzzy logic has now proved worldwide as a tremendous tool to tackle this situation. This paper presents a fuzzy modelling for selection of most economical green building (GB) out of n-alternatives more precisely.
Keywords: attributes, fuzzy decision, TEIV, vague fuzzy EIA, etc.
Similar to Samsa proportional reinsurance_and_probability_of_ruin (20)
Introduction:
RNA interference (RNAi) or Post-Transcriptional Gene Silencing (PTGS) is an important biological process for modulating eukaryotic gene expression.
It is highly conserved process of posttranscriptional gene silencing by which double stranded RNA (dsRNA) causes sequence-specific degradation of mRNA sequences.
dsRNA-induced gene silencing (RNAi) is reported in a wide range of eukaryotes ranging from worms, insects, mammals and plants.
This process mediates resistance to both endogenous parasitic and exogenous pathogenic nucleic acids, and regulates the expression of protein-coding genes.
What are small ncRNAs?
micro RNA (miRNA)
short interfering RNA (siRNA)
Properties of small non-coding RNA:
Involved in silencing mRNA transcripts.
Called “small” because they are usually only about 21-24 nucleotides long.
Synthesized by first cutting up longer precursor sequences (like the 61nt one that Lee discovered).
Silence an mRNA by base pairing with some sequence on the mRNA.
Discovery of siRNA?
The first small RNA:
In 1993 Rosalind Lee (Victor Ambros lab) was studying a non- coding gene in C. elegans, lin-4, that was involved in silencing of another gene, lin-14, at the appropriate time in the
development of the worm C. elegans.
Two small transcripts of lin-4 (22nt and 61nt) were found to be complementary to a sequence in the 3' UTR of lin-14.
Because lin-4 encoded no protein, she deduced that it must be these transcripts that are causing the silencing by RNA-RNA interactions.
Types of RNAi ( non coding RNA)
MiRNA
Length (23-25 nt)
Trans acting
Binds with target MRNA in mismatch
Translation inhibition
Si RNA
Length 21 nt.
Cis acting
Bind with target Mrna in perfect complementary sequence
Piwi-RNA
Length ; 25 to 36 nt.
Expressed in Germ Cells
Regulates trnasposomes activity
MECHANISM OF RNAI:
First the double-stranded RNA teams up with a protein complex named Dicer, which cuts the long RNA into short pieces.
Then another protein complex called RISC (RNA-induced silencing complex) discards one of the two RNA strands.
The RISC-docked, single-stranded RNA then pairs with the homologous mRNA and destroys it.
THE RISC COMPLEX:
RISC is large(>500kD) RNA multi- protein Binding complex which triggers MRNA degradation in response to MRNA
Unwinding of double stranded Si RNA by ATP independent Helicase
Active component of RISC is Ago proteins( ENDONUCLEASE) which cleave target MRNA.
DICER: endonuclease (RNase Family III)
Argonaute: Central Component of the RNA-Induced Silencing Complex (RISC)
One strand of the dsRNA produced by Dicer is retained in the RISC complex in association with Argonaute
ARGONAUTE PROTEIN :
1.PAZ(PIWI/Argonaute/ Zwille)- Recognition of target MRNA
2.PIWI (p-element induced wimpy Testis)- breaks Phosphodiester bond of mRNA.)RNAse H activity.
MiRNA:
The Double-stranded RNAs are naturally produced in eukaryotic cells during development, and they have a key role in regulating gene expression .
Cancer cell metabolism: special Reference to Lactate PathwayAADYARAJPANDEY1
Normal Cell Metabolism:
Cellular respiration describes the series of steps that cells use to break down sugar and other chemicals to get the energy we need to function.
Energy is stored in the bonds of glucose and when glucose is broken down, much of that energy is released.
Cell utilize energy in the form of ATP.
The first step of respiration is called glycolysis. In a series of steps, glycolysis breaks glucose into two smaller molecules - a chemical called pyruvate. A small amount of ATP is formed during this process.
Most healthy cells continue the breakdown in a second process, called the Kreb's cycle. The Kreb's cycle allows cells to “burn” the pyruvates made in glycolysis to get more ATP.
The last step in the breakdown of glucose is called oxidative phosphorylation (Ox-Phos).
It takes place in specialized cell structures called mitochondria. This process produces a large amount of ATP. Importantly, cells need oxygen to complete oxidative phosphorylation.
If a cell completes only glycolysis, only 2 molecules of ATP are made per glucose. However, if the cell completes the entire respiration process (glycolysis - Kreb's - oxidative phosphorylation), about 36 molecules of ATP are created, giving it much more energy to use.
IN CANCER CELL:
Unlike healthy cells that "burn" the entire molecule of sugar to capture a large amount of energy as ATP, cancer cells are wasteful.
Cancer cells only partially break down sugar molecules. They overuse the first step of respiration, glycolysis. They frequently do not complete the second step, oxidative phosphorylation.
This results in only 2 molecules of ATP per each glucose molecule instead of the 36 or so ATPs healthy cells gain. As a result, cancer cells need to use a lot more sugar molecules to get enough energy to survive.
Unlike healthy cells that "burn" the entire molecule of sugar to capture a large amount of energy as ATP, cancer cells are wasteful.
Cancer cells only partially break down sugar molecules. They overuse the first step of respiration, glycolysis. They frequently do not complete the second step, oxidative phosphorylation.
This results in only 2 molecules of ATP per each glucose molecule instead of the 36 or so ATPs healthy cells gain. As a result, cancer cells need to use a lot more sugar molecules to get enough energy to survive.
introduction to WARBERG PHENOMENA:
WARBURG EFFECT Usually, cancer cells are highly glycolytic (glucose addiction) and take up more glucose than do normal cells from outside.
Otto Heinrich Warburg (; 8 October 1883 – 1 August 1970) In 1931 was awarded the Nobel Prize in Physiology for his "discovery of the nature and mode of action of the respiratory enzyme.
WARNBURG EFFECT : cancer cells under aerobic (well-oxygenated) conditions to metabolize glucose to lactate (aerobic glycolysis) is known as the Warburg effect. Warburg made the observation that tumor slices consume glucose and secrete lactate at a higher rate than normal tissues.
Observation of Io’s Resurfacing via Plume Deposition Using Ground-based Adapt...Sérgio Sacani
Since volcanic activity was first discovered on Io from Voyager images in 1979, changes
on Io’s surface have been monitored from both spacecraft and ground-based telescopes.
Here, we present the highest spatial resolution images of Io ever obtained from a groundbased telescope. These images, acquired by the SHARK-VIS instrument on the Large
Binocular Telescope, show evidence of a major resurfacing event on Io’s trailing hemisphere. When compared to the most recent spacecraft images, the SHARK-VIS images
show that a plume deposit from a powerful eruption at Pillan Patera has covered part
of the long-lived Pele plume deposit. Although this type of resurfacing event may be common on Io, few have been detected due to the rarity of spacecraft visits and the previously low spatial resolution available from Earth-based telescopes. The SHARK-VIS instrument ushers in a new era of high resolution imaging of Io’s surface using adaptive
optics at visible wavelengths.
Richard's aventures in two entangled wonderlandsRichard Gill
Since the loophole-free Bell experiments of 2020 and the Nobel prizes in physics of 2022, critics of Bell's work have retreated to the fortress of super-determinism. Now, super-determinism is a derogatory word - it just means "determinism". Palmer, Hance and Hossenfelder argue that quantum mechanics and determinism are not incompatible, using a sophisticated mathematical construction based on a subtle thinning of allowed states and measurements in quantum mechanics, such that what is left appears to make Bell's argument fail, without altering the empirical predictions of quantum mechanics. I think however that it is a smoke screen, and the slogan "lost in math" comes to my mind. I will discuss some other recent disproofs of Bell's theorem using the language of causality based on causal graphs. Causal thinking is also central to law and justice. I will mention surprising connections to my work on serial killer nurse cases, in particular the Dutch case of Lucia de Berk and the current UK case of Lucy Letby.
Comparing Evolved Extractive Text Summary Scores of Bidirectional Encoder Rep...University of Maribor
Slides from:
11th International Conference on Electrical, Electronics and Computer Engineering (IcETRAN), Niš, 3-6 June 2024
Track: Artificial Intelligence
https://www.etran.rs/2024/en/home-english/
Richard's entangled aventures in wonderlandRichard Gill
Since the loophole-free Bell experiments of 2020 and the Nobel prizes in physics of 2022, critics of Bell's work have retreated to the fortress of super-determinism. Now, super-determinism is a derogatory word - it just means "determinism". Palmer, Hance and Hossenfelder argue that quantum mechanics and determinism are not incompatible, using a sophisticated mathematical construction based on a subtle thinning of allowed states and measurements in quantum mechanics, such that what is left appears to make Bell's argument fail, without altering the empirical predictions of quantum mechanics. I think however that it is a smoke screen, and the slogan "lost in math" comes to my mind. I will discuss some other recent disproofs of Bell's theorem using the language of causality based on causal graphs. Causal thinking is also central to law and justice. I will mention surprising connections to my work on serial killer nurse cases, in particular the Dutch case of Lucia de Berk and the current UK case of Lucy Letby.
1. PROPORTIONAL REINSURANCE ON
PROBABILITY OF RUIN IN A SURPLUS
PROCESS COMPOUNDED WITH A
CONSTANT FORCE OF INTEREST
by
Christian Kasumo, MSc, MBA, BSc, Dip Ed
November-December 2011
Centre for ICT Education 1
MULUNGUSHI UNIVERSITY
Pursuing the Frontiers of Knowledge
3. INTRODUCTION
Study considers a diffusion-
perturbated insurance process
compounded with a constant force of
interest.
Overall purpose of the study is to
assess impact of proportional
reinsurance on the ruin probabilities in
this model.
November-December 2011
Centre for ICT Education 3
MULUNGUSHI UNIVERSITY
Pursuing the Frontiers of Knowledge
4. INTRODUCTION (CONTD.)
It is assumed in this study that the
insurance company invests some of its
surplus in a risk-free asset (e.g., a bond)
and that it buys proportional reinsurance
from a reinsurer.
Proportional reinsurance is considered as
opposed to other types of reinsurance as it
is the easiest way of covering an insurance
portfolio.
November-December 2011
Centre for ICT Education 4
MULUNGUSHI UNIVERSITY
Pursuing the Frontiers of Knowledge
5. MODEL
All processes and r.v.’s are defined on a
filtered probability space (Ω,F,{F}tϵR+,P)
satisfying the usual conditions.
The model considered is:
where:
- is the insurer’s
November-December 2011
Centre for ICT Education 5
MULUNGUSHI UNIVERSITY
Pursuing the Frontiers of Knowledge
)()()()(
0
sdRsYtPytY
t
bbb
(1)
)(
1
,)()(
tN
i
iPPP
b
P
bStWbbpttP
6. MODEL (CONTD.)
surplus generating process,
- is the investment generating process,
- is the value of the insurer’s total surplus
just before time t,
- y=Y(0) is the initial surplus or capital of
the insurance company,
- bϵ(0,1] is the retention percentage for
proportional reinsurance,
- bp represents the premium rate net of
reinsurance premiums. If there is no
November-December 2011
Centre for ICT Education 6
MULUNGUSHI UNIVERSITY
Pursuing the Frontiers of Knowledge
rttR )(
)(
tY b
7. MODEL (CONTD.)
reinsurance (i.e., when b=1), then the
premium left to the insurer is simply p, the
premium rate paid by policyholders.
It should be noted that (1) is but an extension
of the Cramér-Lundberg model, for when
σP=r=0 and when b=1, then the model (1)
becomes:
November-December 2011
Centre for ICT Education 7
MULUNGUSHI UNIVERSITY
Pursuing the Frontiers of Knowledge
)(
1
)(
tN
i
iSptytY
8. MODEL (CONTD.)
Definitions
Time of ruin:
Ruin prob.:
where is the survival prob.
Infinitesimal generator of Y is given using Itô’s
formula by
A
November-December 2011
Centre for ICT Education 8
MULUNGUSHI UNIVERSITY
Pursuing the Frontiers of Knowledge
yYtYt bb
b )0(|0)(:0inf
yyYPy bb
b
b
1)0(|
)(1 yy bb
)()()('''
2
1
0
22
sdFygbsygygbpryygbyg
y
P
(2)
9. MODEL (CONTD.)
from which we obtain the relevant Volterra
integro-differential equation (VIDE):
The survival probability satisfies (3)
only if it is strictly increasing, strictly con-
cave and twice continuously differentiable,
and if it satisfies for and
November-December 2011
Centre for ICT Education 9
MULUNGUSHI UNIVERSITY
Pursuing the Frontiers of Knowledge
y
P ysdFbsyybpryyb
0
22
)('''
2
1
(3)
y
0y 0y
10. MODEL (CONTD.)
(Paulsen and Gjessing, 1997).
Theorem: The VIDE (3) can be represented as a
Volterra integral equation (VIE) of the second kind
where the kernel and forcing function are
prescribed and the method of solution of (4) is the
Block-by-Block method, which is considered as the
best of the higher order methods for solving such
equations (Press et al. 1992).
November-December 2011
Centre for ICT Education 10
MULUNGUSHI UNIVERSITY
Pursuing the Frontiers of Knowledge
1lim
y
y
ydsssyKy
y
0
, (4)
23. Ruin probabilities reduce with a
reduction in b (that is, as the
amount reinsured increases), then
start rising again after a certain b.
November-December 2011
Centre for ICT Education 23
MULUNGUSHI UNIVERSITY
Pursuing the Frontiers of Knowledge
RESULTS (CONTD.)
24. We have numerically obtained the
ruin probabilities for a surplus
process compounded with a
constant force of interest
Proportional reinsurance
minimizes the probability of ruin
for insurance companies
November-December 2011
Centre for ICT Education 24
MULUNGUSHI UNIVERSITY
Pursuing the Frontiers of Knowledge
CONCLUSION
25. OPEN PROBLEMS
November-December 2011
Centre for ICT Education 25
MULUNGUSHI UNIVERSITY
Pursuing the Frontiers of Knowledge
Use other forms of reinsurance
(e.g. Excess of Loss, Stop Loss)
Consider investments of Black-
Scholes type in the investment
model
Allow sudden changes (jumps)
in the investment process
26. November-December 2011
Centre for ICT Education 26
Conference organisers
NOMA
Mulungushi University
MULUNGUSHI UNIVERSITY
Pursuing the Frontiers of Knowledge
ACKNOWLEDGEMENTS