Actuarial Study of Life Insurance

Objective

Longevity and mortality risks are both at the heart of current events, the former in particular at the center of pension-related issues, and in the wake of the publication of new prospective mortality tables in France, and the latter following the threats of pandemics or localized epidemics.
Part 1 of this course aims to give an overview of the problems and techniques related to these topics. It will therefore focus on certain life expectancy models, most of which can also be used for disability or invalidity maintenance.
We will then look at methods for developing prospective life tables. We will conclude with an introduction to stochastic mortality models and the mechanisms of longevity risk and mortality risk transfer.
In addition, the entry into force of Solvency 2 on 1 January 2016 imposes new prudential rules on insurers, particularly from a quantitative point of view. It is necessary to set up "economic" balance sheets, i.e. with assets and liabilities on the balance sheet valued at fair value, and to measure the impact on this balance sheet of a catastrophe scenario (occurring once every 200 years). In life insurance, these needs create real technical and operational challenges, due to the complexity of the options supported by the contracts (guaranteed rates, surrender options, etc.).
Part 2 will present the major families of life insurance contracts and the associated risks, and will deal with these new calculation needs and the different methods used by insurers.
The entry into force of Solvency 2 on 1 January 2016 imposes new prudential rules on insurers, particularly from a quantitative point of view. It is necessary to set up "economic" balance sheets, i.e. with a fair value valuation of assets and liabilities on the balance sheet, and to measure the impact on this balance sheet of a catastrophe scenario (occurring once every 200 years). In life insurance, these needs create real technical and operational challenges, due to the complexity of the options supported by the contracts (guaranteed rates, surrender options, etc.).
At the end of this course, students should be able to describe the main characteristics of the different types of life insurance contracts, as well as the assumptions and algorithms used to calculate the value of the insurer's commitments and the capital needs associated with its activity. At the end of this course, students should be able to describe the main characteristics of the different types of life insurance contracts, as well as the assumptions and algorithms used to calculate the value of the insurer's commitments and the capital needs associated with its activity.
Part 3 aims to provide a technical and practical in-depth study of mortality/longevity and long-term care risks, based on recent research work and the current practice of leading players in the insurance market. It is divided into three parts, which cover the entire risk measurement process, from abstract modelling to operational implementation.
At the end of this course, students should be able to present methods for constructing life tables, prospective stochastic mortality models and multi-state models, and detail the implementation of these models in the current regulatory context. These skills will be assessed in writing in a final exam.
 

Planning

Part 1 - Stéphane Loisel

a.    Service life models
b.    Lee-Carter model
c.    Development of prospective life tables
d.    Stochastic mortality
e.    Mechanisms for transferring longevity and mortality risks

Part 2 - Matthieu Chavigny

a.    Portfolio valuation
- Examples of life insurance contracts
- Outcome indicators at the MCEV
- Valuation method for an insurance portfolio
- The Solvency 2 yield curve

b.    Economic Capital
- Economic Capital Solvency II
- Risk modeling
- Dependencies and risk aggregation
- Implementation of an internal model approach
- Economic capital adjustments
- Going further: ORSA and regulatory developments

Part 3 - Alexandre Boumezoued

Tables and templates for biometric risks
a)    Use of national life tables as a basis for calibration and study of their reliability.
b)     The different approaches to measuring the risks of interest in this course:
Stochastic mortality models, their application frameworks and the errors (model and estimation errors) associated with their use,
Multi-state models for measuring dependency risk and estimating impact.
c)    The use of these models to measure risk over a one-year horizon within the current regulatory framework.
 

References

[1] PETAUTON P. (2004). Théorie et pratique de l’assurance-vie, Edition Dunod [36 PET 00 A]. 
[2] DELWARDE A. et DENUIT M. (2006). Construction de tables de mortalité périodiques et prospectives, Economica. [36 DEL 01 A] 
DEVINEAU L., LOISEL S. (2009), Construction d'un algorithme d'accélération de la méthode des « simulations dans les simulations » pour le calcul du capital économique Solvabilité II, Bulletin Français d'Actuariat (BFA), No. 17, Vol. 10, 188-221 DEVINEAU L., LOISEL S. (2009b), Risk aggregation in Solvency II : How to converge the approaches of the internal models and those of the standard formula ?, Bulletin Français d’Actuariat (BFA), No. 18, Vol. 8, 107-145
Part 3 : 
[1] A. Boumezoued, N. El Karoui, S. Loisel. 2015. Measuring mortality heterogeneity dynamics with interval-censored data. HAL preprint Id: hal-01215350
[2] A. Boumezoued. 2016. Improving HMD mortality estimates with HFD fertility data. HAL preprint Id: hal-01270565 2
[3] M. Borger, D. Fleischer and N. Kuksin. 2014. Modeling the mortality trend under modern solvency regimes. Astin Bulletin, 44(01), 1-38.
[4] A.J.G. Cairns. 2000. A discussion of parameter and model uncertainty in insurance. Insurance: Mathematics and Economics 27(3), 313-330.
[5] A.J.G. Cairns, D. Blake, K. Dowd. 2006. A Two-Factor Model for Stochastic Mortality with Parameter Uncertainty: Theory and Calibration. Journal of Risk and Insurance 73(4) 687718.
[6] A.J.G. Cairns, D. Blake, K. Dowd, G.D. Coughlan, D. Epstein, A. Ong, I. Balevich. 2009. A quantitative comparison of stochastic mortality models using data from England and Wales and the United States. North American Actuarial Journal 13(1) 135. 2 [7] A.J.G. Cairns, D. Blake, K. Dowd and A.R. Kessler. 2016. Phantoms Never Die: Living with Unreliable Population Data. To appear in Journal of the Royal Statistical Society, Series A.
[8] C. Czado, A. Delwarde and M. Denuit. 2005. Bayesian Poisson log-bilinear mortality projections. Insurance: Mathematics and Economics, 3 (3), 260-284.
[9] M. Denuit and C. Robert. 2007. Actuariat des Assurances de Personnes. Economica.
[10] Human Mortality Database. University of California, Berkeley (USA), and Max Planck Institute for Demographic Research (Germany). Available at www.mortality.org or www.humanmortality.de (data downloaded on October 2015).
[11] P. Joly, D. Commenges, C. Helmer and L. Letenneur. 2002. A penalized likelihood approach for an illnessdeath model with interval-censored data: application to age-specic incidence of dementia. Biostatistics 3(3) 433443.
[12] N. Keiding. 1990. Statistical inference in the Lexis diagram. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Alexandre Boumezoued 4/5 Engineering Sciences 332(1627) 487509.
[13] R.D Lee, L.R. Carter. 1992. Modeling and forecasting US mortality. Journal of the American Statistical Association 87(419) 659671.
[14] W. Lexis. 1875. Einleitung in die Theorie der Bevolkerungsstatistik. Strassburg: Triibner. (Pages 5-7 translated to English by N. Keytz and printed, with gure 1, in Mathematical Demography (ed. D. Smith & N. Keytz). Berlin: Springer (1977).)
[15] R. Plat. 2011. One-year value-at-risk for longevity and mortality. Insurance: Mathematics and Economics, 49(3), 462-470.659671. [14] W. Lexis. 1875. Einleitung in die Theorie der Bevolkerungsstatistik. Strassburg: Triibner. (Pages 5-7 translated to English by N. Keytz and printed, with gure 1, in Mathematical Demography (ed. D. Smith & N. Keytz). Berlin: Springer (1977).) [15] R. Plat. 2011. One-year value-at-risk for longevity and mortality. Insurance: Mathematics and Economics, 49(3), 462-470.