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Statistics: Understanding & managing the world we live in
                     Actuarial Sciences
    Alumni Politecnico di Milano – Parigi – 22/11/2012
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
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
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
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
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
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
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
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
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
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
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
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
GRAZIE PER L’ATTENZIONE

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Polimi 20121122 r&a

  • 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