The Optimal Strategy Of An Insurer Under Markov-modulated Economy Environment

In this paper, we assume that an insurer can invest in a risky stock and a riskless bond while assuming that the stock price satisfies a Markov-modulated geometrical Brownian motion and the bond price satisfies a Markov-modulated exponential form, that is, the interest rate changes with the economy environment. We mainly study the optimal utility function, the optimal investment strategy and the ruin probability before termination under the above optimal investment strategy. First, we obtain the HJB equation of the optimal utility function using stochastic control method; further, we derive the optimal investment amount in stocks and bonds and also the reinsurance proportion under the assumption that the terminal utility be exponential; then we derive an upper bound for the ruin probability before termination when the insurer adopt the optimal investment and reinsurance strategy which maximizes the exponential utility; in the end, we numerically solve the optimal utility function under a two-state economy environment case, and by using Monte-Carlo simulation on the ruin probability before termination, we illustrate that maximizing exponential utility is strongly positively correlated with minimizing ruin probability.