Stochastic Methods for Insurance

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Life Insurance is by essence a field where stochastic processes can be easily applied. Indeed, a Life Insurance contract can be characterized by two fundamental elements: time and risk: this constitutes precisely the core business of stochastic processes! Life Insurance is also at the conjunction between Insurance and Finance. Life products contain often a crucial saving aspect but simultaneously they are generally based on various insurance risks (mortality, longevity, disability, long term care). Random techniques inspired by modern quantitative finance as well as by actuarial theory are therefore largely used. The purpose of this book is to show how stochastic processes develop, and can lead to various stochastic methods applied to life insurance, in order to price, valuate, hedge and manage these contracts. This random perspective becomes particularly essential nowadays in the context of SOLVENCY II which requires sound risk management modelling. In this context, in contrast with the traditional way in actuarial science to model life insurance (constant discount rate mixed with a fixed deterministic life table), modern approaches incorporate the stochastic nature of these elements.