Optimal Investment Strategy Option For Insurance Company

The wealth of the insurance company is not only dependent on its insurance business,as well as its assets for a reasonable investment. With the increase of insurance compa-nies engaged in risk investment activities, the choice of optimal investment strategy attractedmore and more attention of researchers. There are two main research fields from the exist-ing literature: one is to maximize the expect wealth of the insurance companies;another isto minimize the ruin probability. In either situation, it is difcult to calculate the optimalinvestment strategy directly. We consider a stochastic model for the wealth of an insurancecompany which has the possibility to invest into risky investment and insurance business. Weconsider the optimal investment strategy under the two diferent regimes which maximizesthe expected wealth of the insurance company and minimized the ruin probality of the riskprocess.In the first regime, we suppose the price of the risky asset follows a general exponentialLévy process, we investigate the resulting reserve process and the corresponding discountednet loss process with the standard methods from the theory of stochastic recurrence equation-s. This opens up a way to measure the risk and we provide an approximation of the optimalinvestment strategy under a risk constraint on the Value-at-Risk.In the second regime, we consider a risk process modelled as a compound Poisson pro-cess, the optimal strategy is computed using the Bellman equation. We prove the existenceof a solution and give the analytic expression of the optimal investment strategy.