This document discusses the role of actuaries and statistical modeling. It explains that actuaries at R&A use both deterministic and stochastic models to analyze insurance portfolios, assess risks, set prices, and ensure sufficient capital reserves. Deterministic models provide single estimates while stochastic models account for uncertainty through probability distributions. The document also summarizes the upcoming Solvency 2 regulation in Europe and the gender directive banning gender-based insurance pricing. It provides references for further reading on these actuarial topics.

1. Statistics: Understanding & managing the world we live in
Actuarial Sciences
Alumni Politecnico di Milano – Parigi – 22/11/2012

2. Statistics: Understanding & managing the world we live in : Actuarial sciences
What an actuary do in R&A?
Deterministic Versus Stochastic
Solvency 2, what’s this?
21/12/2012 Gender directive : the end of gender-based pricing
References
Polimi Parigi 22/11/2012 - R&A – Lionel Texier - Associate director

3. Statistics: Understanding & managing the world we live in : Actuarial sciences
What we do ?
• Implementation, audit & reviews of
models
• Insurance portfolio analysis & product
engineering
• Process engineering
• Enterprise Risk Management expertise
• Asset-Liability Management
• Pension & Benefits advisory services
• CRM
• Data Mining
• R&D
• Training
Polimi Parigi 22/11/2012 - R&A – Lionel Texier - Associate director

4. Statistics: Understanding & managing the world we live in : Actuarial sciences
What an actuary do in R&A?
Deterministic Versus Stochastic
Solvency 2, what’s this?
21/12/2012 Gender directive : the end of gender-based pricing
References
Polimi Parigi 22/11/2012 - R&A – Lionel Texier - Associate director

5. Statistics: Understanding & managing the world we live in : Actuarial sciences
Deterministic Versus Stochastic
• Deterministic model : use single best-estimate
parameters to produce a single best-estimate
of the probable outcome
• A deterministic calculation assumes that there
is only one way for the future
• Pros : it is simple
• Cons : Is it always enough & realistic?
• Example : will a 70 years old woman life
expectancy be the same in 2050 compare to
2012?
• What will be the yield curve in 5 years? Will it
be different compare to the current zero
coupon yield curve?
Polimi Parigi 22/11/2012 - R&A – Lionel Texier - Associate director

6. Statistics: Understanding & managing the world we live in : Actuarial sciences
Deterministic Versus Stochastic
• Stochastics models : deliver full probability
distributions of potential outcomes that include
A scenario of the death rate surface
random variable in one or more of the parameters
Source : http://freakonometrics.blog.free.fr
• A stochastic calculation is the study of a time
dependent random variable
• Advantage : an exhaustive risk-based approach is
possible
• Example : how much capital an insurance
company should hold if we want to prevent its
failure over the year in 99,5% of the cases ?
• Limits : what happened if the model is wrong? A
model will always be a simplification of a more
complex reality? The statistician must never be
totally confident in the model and at the end, the
man make the decision
Polimi Parigi 22/11/2012 - R&A – Lionel Texier - Associate director

7. Statistics: Understanding & managing the world we live in : Actuarial sciences
What an actuary do in R&A?
Deterministic Versus Stochastic
Solvency 2, what’s this?
21/12/2012 Gender directive : the end of gender-based pricing
References
Polimi Parigi 22/11/2012 - R&A – Lionel Texier - Associate director

8. Statistics: Understanding & managing the world we live in : Actuarial sciences
Solvency 2 : what’s this?
What about the European directive What should the stakeholders expect of
2009/138/CE? Solvency 2?
• 3 pillars of quantitative and qualitative rules •  A standardization of rules accross EU
• A risk-based capital framework and holistic •  More transparency and a guarantee of a
approach : the P&L is a assumed to be a better gouvernance
multivariate random variable •  Early warning in case of trouble
• The Solvency 2 project is in line with Basel 2, it •  will S2 be effective during or after the end
is not applied yet of the crisis
• Insurance companies invest a lot of money to •  systemic risk impulsed by S2?
implement Solvency 2, it is a very big project •  an increase of procyclicality for insurance
for the insurance industry market?
• Despite the Basel 2 system, the banking •  an increase of insurance premium on a
industry is closed to a catastrophic collapse, short-middle term even if S2 would impact
what about Solvency 2? would be positive on the long term view
Polimi Parigi 22/11/2012 - R&A – Lionel Texier - Associate director

9. Statistics: Understanding & managing the world we live in : Actuarial sciences
Risk-based capital : a risk measure
Marginal distribution of each random variable Correlation & dependence
To choose the random variable
To set the parameters
What are the correlations
between variables?
To choose the percentile
In the standard formula of S2, we
To choose the measure:
use the VaR 99,5% over a year,
VaR? TVaR?
and we assume a multivariate
normal distrubution with linear
correlations
For example the required capital should be at least equal to
the 99,5% worst variation of the net asset value over a given
period (1 year for S2)
Polimi Parigi 22/11/2012 - R&A – Lionel Texier - Associate director

10. Statistics: Understanding & managing the world we live in : Actuarial sciences
What an actuary do in R&A?
Deterministic Versus Stochastic
Solvency 2, what’s this?
21/12/2012 Gender directive : the end of gender-based pricing
References
Polimi Parigi 22/11/2012 - R&A – Lionel Texier - Associate director

11. Statistics: Understanding & managing the world we live in : Actuarial sciences
Gender Directive
What about the European directive What should the consumers expect of the
2004/113/CE? Gender Directive?
• The end of gender-based pricing • Motor insurance premium would increase
• Whatever the change in the pricing strategy of • Death insurance premium would increase
insurers, IT systems will be impacted by the • Annuity premium would decrease
different treatment of new business
• Increase of adverse selection, moral hazard & • Motor insurance premium would decrease
insurance exclusion
• Death insurance premium would decrease
• Risk of change of the market equilibrium,
potential impact on the socio-economic • Annuity premium would increase
consumer behaviour
• Gender-based risk management & marketing is • Redistribution effects
still possible • One-off compliance & marketing costs
• Will unisex insurance pricing be combined with • Gender mix risk premium
less discrimination on other fields? Not sure
Polimi Parigi 22/11/2012 - R&A – Lionel Texier - Associate director

12. Statistics: Understanding & managing the world we live in : Actuarial sciences
What an actuary do in R&A?
Deterministic Versus Stochastic
Solvency 2, what’s this?
21/12/2012 Gender directive : the end of gender-based pricing
References
Polimi Parigi 22/11/2012 - R&A – Lionel Texier - Associate director

13. Statistics: Understanding & managing the world we live in : Actuarial sciences
References
Actuary : R&A:
• http://www.italian-actuaries.org • www.riskandanalysis.com
• http://www.institutdesactuaires.com • Lionel.texier@riskandanalysis.com
• http://www.actuaries.org/
Cocktail ActuariaCnam 12.12.12:
European Insurance supervisor :
• http://cocktail-actuariacnam.evenium.net
• https://eiopa.europa.eu/
Blogs :
Gender Directive :
• www.techsandtools.com
• http://genderdirective.actuariacnam.net • http://freakonometrics.blog.free.fr
• Official text • www.actuariacnam.net
Solvency 2: Books :
• www.lalibrairieducnam.fr
• http://forumactuariat2011.actuariacnam.net • (please visit the EMS/Assurance/actuariat category )
Polimi Parigi 22/11/2012 - R&A – Lionel Texier - Associate director

14. GRAZIE PER L’ATTENZIONE