Pricing and risk minimizing hedging strategies for multiple life unit linked insurance policies using constant proportion portfolio insurance approach

Jafarova, Vafa
A unit-linked life insurance policy (ULIP) is an agreement between an insurer and an insured that the insurance benefits or the obligations of the insurance company depend on the price of some specified stocks. As opposed to the classical life insurance, the payments to be paid at the occurrence of risk or at the end of the period of a unit linked life insurance contract can not be known at the time the policy is sold. Therefore, the benefits are random and unknown in advance, and based on this the obligations of the insurance company are also random. The main purpose in such a situation is to correctly define obligations of the insurance company, and based on these obligations to define the proper hedging approach. In this thesis, we consider a model which takes into consideration the uncertainty of financial market and portfolio of insured individuals at the same time. It is assumed that financial and the insurance portfolios are stochastically independent and considered to be combined in a common product probability space. For the insurance portfolio under concern, we assume that polices are independent, but lifetimes of insureds in each policy are dependent. For the dependency between the lifetimes of insureds, an appropriate Pseudo-Gompertz distribution is used in the thesis. We investigate two cases for multiple life policies, joint life status and last-survival status. Appropriate obligation equations for both cases are derived and by the Constant Proportion Portfolio Insurance (CPPI) approach optimal portfolio weights are defined. For the solution of optimization problem, mean-variance hedging strategy is used as one of the mostly applied hedging approaches in such situations. The thesis ends with a conclusion and an outlook to future studies.