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本文对跳-扩散风险模型,在赔付进行比例再保险,以及盈余投资于无风险资产和风险资产的条件下,研究使得最终财富的指数期望效用最大的最优投资和比例再保险策略.得到最优投资策略和最优再保险策略,以及最大指数期望效用函数的显式表达式,发现最优策略和值函数都受到无风险利率的影响.最后通过数值计算,得到最优投资和比例再保险策略,以及值函数与模型各个参数之间的关系.
This paper studies the optimal investment and proportional reinsurance strategies that maximize the exponential expectation of the ultimate wealth under the conditions of the jump-diffusion risk model, the proportional reinsurance payment and the surplus investment in risk-free assets and risky assets. The optimal investment Strategy and optimal reinsurance strategy as well as the explicit expression of the maximum expected utility function, it is found that both the optimal strategy and the value function are affected by the risk-free interest rate.Finally, we get the optimal investment and proportional reinsurance strategy by numerical calculation, Relationship between function and model parameters.