Du 10 au 12 juillet 2019, se tient à Munich la 23ème édition du International Congress on Insurance: Mathematics and Economics.
A cette occasion, Stéphane Loisel et Patrick Laub, chercheurs membres de la Chaire DAMI, présenteront leurs travaux respectifs :
Quickest change detection problem and longevity applications
Nicole El Karoui, Sorbonne Universites, Stephane Loisel, Universite Lyon 1, Yahia Salhi, Universite Lyon 1
In this talk, we present quickest change detection problem: how to detect as quickly as possible that actuarial assumptions are not satised anymore due to a structural change in the mortality patterns, or due to the materialization of level risk or basis risk? We show that the so-called cusum strategy is optimal in a generalized Lorden sense, and present implementation challenges for longevity and mortality monitoring applications. This talk is based on a joint work with Nicole El Karoui and Yahia Salhi.
Phase-Type Models in Life Insurance: Fitting and Valuation of Equity-Linked Benefits
Søren Asmussen, Aarhus University, Patrick J. Laub, Université Lyon 1, Hailiang Yang, Hong Kong University
Phase-type (PH) distributions are dened as distributions of lifetimes of finite continuous-time Markov processes. Their traditional applications are in queueing, insurance risk, and reliability, but more recently, also in finance and, though to a lesser extent, to life and health insurance. The advantage is that PH distributions form a dense class and that problems having explicit solutions for exponential distributions typically become computationally tractable under PH assumptions. The fitting of PH distributions to human lifetimes is considered, and some new software is developed. The pricing of life insurance products such as guaranteed minimum death benefit and high-water benefit is treated for the case where the lifetime distribution is approximated by a PH distribution and the underlying asset price process is described by a jump diusion with PH jumps. The expressions are typically explicit in terms of matrix-exponentials involving two matrices closely related to the Wiener-Hopf factorization, for which recently, a Lévy process version has been developed for a PH horizon. The computational power of the method of the approach is illustrated via a number of numerical examples.