The Optimal Investment In Security Market With Jumps For Insurer

In this paper we investigate the optimal investment for an insurer in the security market with jumps .In the past ,the price of stock is modeled by a geometrical B.M.and now it is modeled by a exponential-Levy process which is more accurate in my paper. Most people investigated the optimal investment problem of mean-variance for an insurer via a control theory while the martingale approach has been widely used in mathematical finance.In this paper we obtain the closed-form solutions to the problem of mean-variance efficient investment by the martingale approach. The effect of the claim processes and jump processes of stock price on the mean-variance efficient strategies and frontier is also analyzed which is as follow :1.When the cumulative amount of the claims increases,if the average increase rate of the stocks is higher than the risk-free interest rate.the insurer will choose to hold more stocks,on the contrary,the insurer will choose to hold less stocks. 2.When the cumulative amount of the price jumps of the stocks increases,if the average increase rate of stocks is higher than the risk-free interest rate,the insurer will choose to hold more stocks,on the contrary,the insurer will choose to hold less stocks.3.The correlation coefficient of the security market and the risk process of the insurer is higher,the risk confronted by the insurer is higher. For the CARA,we still investigate it although the solutions we obtain under it is absolutely independent of the processes with jumps.This is because it is still an efficient approach of the portfolio selection for an insurer. In the end we continue to investigate the optimal investment under CARA for an insurer by the martingale approach.