Optimal Investment Strategy Under Excess-of-loss Reinsurance

In resent years, the optimal reinsurance and investment related issues has attracted increasing attention in finance. The insurance industry is highly competitive, to enhance the competitiveness of enterprises, on the one hand, insurance companies need to invest in the financial markets, which can improve the company’s solvency and efficiency, and investment is one of the main channels for insurance companies to obtain funds. On the other hand, in order to reduce the risk of compensation too much, the insurer needs to purchase reinsurance and make risk diversion among insurance companies, which can promote stability of the insurance industry, and to achieve of benefit-sharing and risk-sharing. Above all, to study the issue of optimal investment and reinsurance strategies has a very important practical significance for the insurance company.In this paper, we study optimal excess-of-loss reinsurance and investment strategies of an insurer with jump diffusion risk process. The insurer can invest in a risk-free asset and a risky asset, and allowed to buy excess-of-loss reinsurance to reduce risk. Our main objective is to find the optimal investment and reinsurance strategies which minimize ruin probability of insurer. By applying the diffusion approximation approach, we obtain the close form expression of the optimal policy, and find that optimal strategy and ruin probability are affected by the risk-free interest rate. Finally, some numerical examples are given, which illustrate the effects of the parameter on the optimal reinsurance-investment strategy and the corresponding minimal ruin probability.