Time consistent risk measures for long-term life insurances and pension products

A quite important issue for a life insurance undertaking or concerning pension benefits is the determination of the solvency capital, i.e. the capital the insurer has to put aside in order to be solvent according to a solvency measure used by its regulatory authority. The nub of the problem lies in the computation of this capital and in the long-term characteristic of some life insurance products. This topic has become of paramount importance over the past decade due to the last crises arising from the banking sector, and following the introduction of the new European regulatory framework for the insurance sector, Solvency II. The aim of this thesis is to compare different methods which take into account the time horizon of the liability in the computation of the solvency capital. We first start with a static approach with risk measures. However, for pension liabilities with long-term horizons, the information disclosed through time could be meaningful and should be considered in the computation of the capital. We then study time consistent dynamic risk measures and finally introduce a new construction of such a measure.