This paper studies an optimal excess-of-loss reinsurance and investment problem with thinning dependent risks. Assume that the insurer’s wealth process is described by a risk model with two dependent classes of insurance business, and the insurer is allowed to purchase excess-of-loss reinsurance from the reinsurer and invest in a risk-free asset and a risky asset whose price follows Heston model. Our aim is to seek the optimal excess-of-loss reinsurance and investment strategy under the criterion of maximizing the expected exponential utility of the terminal wealth. Applying Legendre transform along with the stochastic control theory, we obtain the explicit expressions of the optimal excess-of-loss reinsurance and investment strategy. Finally, we give some numerical examples to illustrate our results.

本文研究了具有变薄依赖性风险的最优损失超额再保险和投资问题。假设保险人的财富过程由具有两种相关保险业务类别的风险模型来描述，并且允许保险人从再保险人购买超额亏损再保险，并投资于无风险资产和风险资产的价格遵循Heston模型。我们的目标是在最大化终端财富的预期指数效用的标准下寻求最优的超额损失超额再保险和投资策略。结合Legendre变换和随机控制理论，我们得到了最优损失超额再保险和投资策略的明确表示。最后，我们给出一些数值示例来说明我们的结果。