Statistics: Understanding & managing the world we live in

Actuarial Sciences

Alumni Politecnico di Milano – Parigi – 22/11/2012

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

Statistics: Understanding & managing the world we live in : Actuarial sciences

References

Polimi Parigi 22/11/2012 - R&A – Lionel Texier - Associate director

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

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

Statistics: Understanding & managing the world we live in : Actuarial sciences

References

Polimi Parigi 22/11/2012 - R&A – Lionel Texier - Associate director

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

Statistics: Understanding & managing the world we live in : Actuarial sciences

Deterministic Versus Stochastic

• Stochastics models : deliver full probability distributions of potential outcomes that include random variable in one or more of the parameters

• 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

A scenario of the death rate surface Source : http://freakonometrics.blog.free.fr

Polimi Parigi 22/11/2012 - R&A – Lionel Texier - Associate director

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

Statistics: Understanding & managing the world we live in : Actuarial sciences

References

Polimi Parigi 22/11/2012 - R&A – Lionel Texier - Associate director

Solvency 2 : what’s this?

What about the European directive 2009/138/CE?

• 3 pillars of quantitative and qualitative rules

• A risk-based capital framework and holistic approach : the P&L is a assumed to be a multivariate random variable

• The Solvency 2 project is in line with Basel 2, it is not applied yet

• Insurance companies invest a lot of money to implement Solvency 2, it is a very big project for the insurance industry

• Despite the Basel 2 system, the banking industry is closed to a catastrophic collapse, what about Solvency 2?

What should the stakeholders expect of Solvency 2?

• A standardization of rules accross EU

• More transparency and a guarantee of a better gouvernance

• Early warning in case of trouble

• will S2 be effective during or after the end of the crisis

• systemic risk impulsed by S2?

• an increase of procyclicality for insurance market?

• an increase of insurance premium on a short-middle term even if S2 would impact would be positive on the long term view

Polimi Parigi 22/11/2012 - R&A – Lionel Texier - Associate director

Statistics: Understanding & managing the world we live in : Actuarial sciences

Risk-based capital : a risk measure

To choose the random variable

To set the parameters

To choose the percentile

To choose the measure: VaR? TVaR?

Marginal distribution of each random variable Correlation & dependence

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)

In the standard formula of S2, we use the VaR 99,5% over a year, and we assume a multivariate normal distrubution with linear correlations

Polimi Parigi 22/11/2012 - R&A – Lionel Texier - Associate director

Statistics: Understanding & managing the world we live in : Actuarial sciences

What are the correlations between variables?

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

Statistics: Understanding & managing the world we live in : Actuarial sciences

References

Polimi Parigi 22/11/2012 - R&A – Lionel Texier - Associate director

Gender Directive

What about the European directive 2004/113/CE?

• The end of gender-based pricing

• Whatever the change in the pricing strategy of insurers, IT systems will be impacted by the different treatment of new business

• Increase of adverse selection, moral hazard & insurance exclusion

• Risk of change of the market equilibrium, potential impact on the socio-economic consumer behaviour

• Gender-based risk management & marketing is still possible

• Will unisex insurance pricing be combined with less discrimination on other fields? Not sure

What should the consumers expect of the Gender Directive?

• Motor insurance premium would increase

• Death insurance premium would increase

• Annuity premium would decrease

• Motor insurance premium would decrease

• Death insurance premium would decrease

• Annuity premium would increase

• Redistribution effects

• One-off compliance & marketing costs

• Gender mix risk premium

Polimi Parigi 22/11/2012 - R&A – Lionel Texier - Associate director

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

Statistics: Understanding & managing the world we live in : Actuarial sciences

References

Polimi Parigi 22/11/2012 - R&A – Lionel Texier - Associate director

References

Polimi Parigi 22/11/2012 - R&A – Lionel Texier - Associate director

Statistics: Understanding & managing the world we live in : Actuarial sciences

Actuary : • http://www.italian-actuaries.org • http://www.institutdesactuaires.com • http://www.actuaries.org/

European Insurance supervisor : • https://eiopa.europa.eu/

Gender Directive : • http://genderdirective.actuariacnam.net • Official text

Solvency 2:

• http://forumactuariat2011.actuariacnam.net

R&A: • www.riskandanalysis.com • Lionel.texier@riskandanalysis.com

Cocktail ActuariaCnam 12.12.12: • http://cocktail-actuariacnam.evenium.net

Blogs : • www.techsandtools.com • http://freakonometrics.blog.free.fr • www.actuariacnam.net

Books : • www.lalibrairieducnam.fr • (please visit the EMS/Assurance/actuariat category )

GRAZIE PER L’ATTENZIONE