Optimal Policies Problem For An Insurer With HARA And Piecewise Utility Function

The thesis mainly discussed the insurers' optimal investment and risk control strategies in an incomplete markets.We assumed that insurers invested in various risky assets,the price process was depicted by Geometric Brownian motion,and the payment process for each claim was described by a process of compound Poisson process with drift.The insurer controlled their risk of profits through changing the number of policies and the total risky assets allocation.As is known to all that in the incomplete market,martingale method could not be utilized directly to solve optimal problem,we ought to complete this market.Firstly,constructed the new Brownian motion which makes the dimension equal to the amount of risky assets.Secondly,based on the principle of maximizing the expected utility of terminal wealth,and in view of the optimal strategy of hyperbolic absolute risk aversion(HARA)utility function,the thesis contrasts the coefficient which is calculated by Martingale representation theorem and It?o formula,and got the optimal strategy.Finally,we assumed that the insurers were irrational investors who were loss aversion,and in view of the optimal strategy of piecewise utility function,the thesis translated the dynamic optimization problem into a static optimization problem with the help of the martingale method.This problem were solved by Lagrange multiplier and gained the optimal strategies.