Optimal investment and reinsurance under partial information and loss aversion
This paper studies the optimal investment and reinsurance strategy for an loss-aversed insurer under partial information.First,the filtering technique is used to transform the problem.Then,under the expected SS-shaped utility maximization criterion,the semi-analytical expression of optimal investment and reinsurance strategy is derived by using martingale method,partial differential equation,Fourier transform and inverse transform method.Finally,the Monte Carlo method is used in the numerical analysis.The results show that the optimal ratios of investment and reinsurance under ignoring learning are lower than that under filtering estimation.When the reference point level is higher,compared with the ratios of optimal reinsurance and investment in inflation index bond,ignoring learning has a greater effect on the optimal ratio of investment in stock.On the other hand,the optimal strategy under the power utility is more aggressive than the optimal strategy under the S-shaped utility,and the optimal reinsurance ratio has the largest difference under the two types of utility functions,which shows that psychological factors have the most significant impact on the reinsurance strategies.
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