Relatore
Alessandra Cretarola - Università di Perugia
Abstract
We study the problem of hedging unit-linked life insurance contracts in incomplete markets when there are restrictions on the available information by using the local risk-minimization approach. This type of insurance contract is closely related to the financial market since benefits depend on the development of a certain stock price. Then, it makes sense to consider the combined model given by the underlying semimartingale model of financial market and the insurance portfolio. Firstly, we refer to the case of complete information on the insurance portfolio and a limitative knowledge on the financial market. More precisely, we assume that, at any time, the insurance company has access to the information about the number of policy-holders who are still alive but it has a partial information about the stock prices. We characterize the risk-minimizing hedging strategy for pure endowment contracts when the underlying price process is expressed in units of the numéraire portfolio and the mortality hazard rate is a deterministic function, and then we compute it explicitly in a Markovian jump-diffusion driven market model. Next, we consider the case where there are restrictions on the information concerning the insurance portfolio. In particular we assume that, at any time, the insurance company has a complete knowledge of the financial market and may observe the number of deaths from a specific portfolio of insured individuals but not the mortality hazard rate, which may depend on unobservable exogenous stochastic factors. We characterize the locally risk-minimizing hedging strategy for pure endowment and term insurance contracts in terms of the projection of the survival process on the information flow. Finally, we see that in a Markovian framework, this leads to a filtering problem with point process observations. The talk is based on joint works with Claudia Ceci and Katia Colaneri
Organizzatore: Sabrina Mulinacci.