Mathematical Modelling of the Discrete Time Investment Strategy of Insurance Companies

Abstract

The target of the insurance companies is to manage the risk of losses (in the form of wealth or health etc.) of their clients. The clients pay premiums to the companies to buy a policy while the companies invest the collected premiums in markets (risky/non-risky) to handle the risks. Continuous time trading investment strategies are modeled by several authors but no body can trade continuously. A discrete time investment mathematical model to deal with this kind of business has been introduced. For this purpose, firstly, an upper bound of the claim size has been calculated. Secondly, explicit form of ruin probability function has been studied. It has been observed that this ruin probability is less than one. It has been shown that the function is decreasing and smooth with respect to premium parameters satisfying second order partial differential equation having bounded second derivative with respect to initial wealth.
The obtained results can be used for the identification of optimal claim size, financial market, optimal investment strategies and the optimal investment time to reduce ruin of the companies.