Optimal Investment Strategy For Insurer In A Jump-diffusion Market With No Short-selling

Since funds of the insurance are allowed to invest directly into the stock market,the problem of investment of insurance funds has become one focus of theoretical research.By the end of 2014,total assets of the insurance industry have exceeded 10 trillion yuan.In order to realize the value of insurance funds,the best way is to invest.Ensuring that the investment of funds has a certain return on investment,how to make investment risks to the minimum become critical problems.Although some scholars has been analyzed such issues by the traditional mean-variance model,they did not consider the investment market in our country is under no short-selling constraints.In addition,more and more empirical analysis shows that returns and the volatility of China's stock market are following jump-diffusion process.Therefore,in this article,we study the problem of optimal investment strategy for an insurer in the condition the risk assets follow the jump-diffusion process and the stock market is not allowed short selling.In this article,we assume that the surplus of insurance company follows compound Poisson process(the classic Lundberg-Cramer process)and the risky assets follow a jump-diffusion process.Insurance funds are invested continuously to a risk-free asset and n risky assets,and the prices of risky assets follow the jump-diffusion process.First of all,based on the mean-variance optimization rules,investment model under no short-selling constraints is established,then using theory of dynamic programming principle and viscous solution to solve the model,the explicit and closed formula of the optimal investment strategy and the efficient frontier are derived;Secondly,cosid-ering that insurance company run with the indebtedness and require more of security,we assume the company should choose proportion of its initial capital which consiste-nt with their investment period for venture investment.Build a model contains safety investment proportion,and also use the dynamic programming principle to get the optimal investment strategy and the efficient frontier.Finally,effects of parameters such as the premium rate,the claim amount and intensity on the optimal investment strategy and the efficient frontier are analyzed through numerical simulation ways which may provide theoretical support for insurance company's investment Results show that optimal investment strategy under no short-selling condition and the factors such as initial capital,the premium rate is not simple negative or positive correlation,but divided into strict limits on the size of investment region and decrease(increase)region with the lever of initial capital.