The ANR project LoLitA 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.
Coordination of the project: Stéphane Loisel
Coordinator: Nicole El Karoui
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.
Coordinator: Christian Robert
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.
Coordinator: Gilles Pagès
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...).
Coordinator: Stéphane Loisel
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 behavioral risk associated with pension and long term care insurance.
Coordinators: Paul Doukhan and Matthieu Rosenbaum
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.
Coordinator: Ragnar Norberg
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 payment 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 intergenerational risk sharing is proposed and examined.