Pricing, design and solvency measurement of annuity products

In the well-known context of the population ageing and the need for pensions funding, life annuity products occupy a very important place as natural hedging for policyholders against longevity risk. In particular, the difficulties of pay-as-you-go schemes and the need to provide funding for dependency of elderly are important factors motivating the study of life annuity as solutions to these. However, these products pose many actuarial and financial challenges, especially given their long-term nature. A precise analysis of these products indeed requires taking into account diverse risks such as interest rate, equity, longevity over periods of time that can be counted in decades depending on the nature of the product. The new European solvency regulations require financial operators to provide a minimum capital upon their insurance commitments, called the solvency capital. Determining this capital in an adequate way is particularly difficult for long-term products. The objective of this thesis is on the one hand, to propose suitable single-risk and multi-risks models, based on investment strategies for assessing the solvency capital of an insurer selling annuities. This will thus ensures regular payment of benefits to the policyholders while they are alive, in accordance with both the regulation requirements and the type of annuity traded. We achieve this for classical annuities such as lifetime, deferred and term annuities. On the other hand, another objective is to study the valuation and actuarial design of life annuity products and to propose new methods of risk sharing between policyholders and insurers. To do so, risk-linked annuity products will be analyzed, particularly the group self-annuitization with a focus on interest rate, equity and longevity risks.