Optimal investment portfolio for a dynamic life insurance product using stochastic control approach

 In this article, a life insurance product is designed with the help of stochastic control approach. These products are defined in such a way that in exchange for receiving an amount as insurance premium that is paid at specified times, the insurer undertakes to pay insurance benefits when the insured is alive at the end of the contract.

This research is an analytical study in terms of developmental-applicative purpose. In the literature of life insurance, there are various products that are not the same in the type of benefit payment and the timing of their implementation. Among these examples, term life insurance, term life insurance, and mixed life insurance can be mentioned. Traditional insurance products with fixed benefits are quickly losing their appeal due to inflationary markets. In this research, it is focused on the design of a life insurance product on the condition of life, which is connected to the investment markets. Stochastic differential calculus models have been used to simulate capital markets assets. All the numerical results of this research have been calculated with the help of Matlab and Maple software.

To achieve the best choice of investment type, with the help of stochastic optimal control tool, the best investment strategy was calculated for a person who has the CRRA utility function and buys this product, so that the most benefits are paid at the end of the contract. To invest in this contract, modeling was done in a non-risky market such as a bank and a risky market such as stocks, which have price jumps. In addition, to model the risk asset, the Merton model, which is a representative of the models with finite activity, was used, and at the end, a comparison was made for several mortality functions.

The main purpose of this article is investment for the insured who bought this product. In the product designed in this article, the insurer undertakes to pay the premiums received at a guaranteed rate at the end of the contract. Also, the insured will share the profit from the investment based on a certain percentage that is determined at the beginning of each year. The simulations show that the behavior of the optimal consumption rate is the same as the Merton model with the approach that the behavior of full price jumps is transparent in the optimal consumption rate designed in this article. Investment results for several mortality functions are reported in the Numerical Results section.