Blanc SIMI 1 - Blanc - SIMI 1 - Mathématiques et interactions

Dynamic models for human LOngevity with LIfesTyle Adjustments – LoLitA

Submission summary

The present project aims to develop models for the uncertain long term development of human longevity and methods for managing longevity-related risk in pensions and long term health care.
From a mathematical point of view, this requires advances in stochastic models for population dynamics and in certain classes of semi-Markov models, development of advanced numerical methods for such models, and development of new statistical methods (online change-point detection, calibration issues in longevity and long term care models,...).
The project is composed of six interconnected tasks, concerning respectively population dynamics modeling, long term care contracts, advanced simulation methods, multi-year solvency issues and joint stress tests, statistical aspects of longevity risk, and finally management of longevity risk in pensions.
The first task is devoted to stochastic models for population dynamics, which go beyond the deterministic models used in demography. Inspired by recent advances in the field of ecology, especially Individual-Based Models, we are interested in constructing and studying particle systems including specific individual characteristics, suited to the analysis of short and long-term longevity risk.
In the second task, we introduce multi-state processes with path-dependent intensities (semi-Markov and beyond) for actuarial analysis of various forms of long term care insurance.
Stochastic models for longevity and long-term care are computationally demanding. The third task is devoted to advanced simulation methods for population dynamics models of high complexity. These models are applied to actuarial products (life insurance, variable annuities, etc) with excessively long maturities, hence also simulation time. We will devise, adapt or transfer advanced sophisticated techniques (extrapolation, variance reduction, semi-closed forms, quasi-Monte Carlo) to provide a flexible and powerful simulation toolbox (fast computation, rare events, local refinements, etc...).
In the fourth task, we consider average and long-term solvency issues, and develop extreme scenario generators and joint stress tests for longevity and long term care. We also study aspects of behavioral risk associated with pension and long term care insurance.
In the fifth task, we address various statistical issues that arise in the context of longevity. Our goal is to introduce new statistical procedures for various types of models for mortality, longevity, and population dynamics. These methods will partly rely on extreme value theory, change point detection techniques, estimation procedures for stochastic differential equations, and bootstrap methods.
In the last task, we revisit the traditional paradigm of life insurance, whereby non-diversifiable economic and demographic risk was shared by the insured. A solution with index-linked payments is proposed. A unified approach is taken to the with-profit scheme, encompassing all forms of bonuses, and pursuing ideas of experience-based first-order technical basis and optimal bonus schemes. An extension to inter-generational risk sharing is proposed and examined.
To sum up, we consider { f in some integrated way} important sources of longevity and long-term care risks, their
representation with innovative models, their estimation, the way they can be analyzed by new mathematical techniques and computed through advanced simulations and other numerical methods.
The mathematical models are aimed at generality and unification, and their applications are aimed to be timely, addressing current risk management issues in longevity, long-term care, and pensions.

Project coordinator

Monsieur Stéphane LOISEL (Laboratoire de Sciences Actuarielle et Financière)

The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.

Partner

LPMA Laboratoire de Probabilités et Modélisation Aléatoire
SAF Laboratoire de Sciences Actuarielle et Financière

Help of the ANR 290,000 euros
Beginning and duration of the scientific project: November 2013 - 48 Months

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