In this paper, we investigate the problem of optimal strategies of dividend and reinsurance under the Cramer-Lundberg risk model embedded with the thinning-dependence structure which was firstly introduced by Wang and Yuen (2005), subject to the optimality criteria of maximizing the expected accumulated discounted dividends paid until ruin. To enhance the practical relevance of the optimal dividend and reinsurance problem, non-cheap reinsurance is considered and transaction costs and taxes are imposed on dividends, which converts our optimization problem into a mixed classical-impulse control problem. For the purpose of better mathematical tractability and neat, explicit solutions of our control problem, instead of the Cramer-Lundberg framework we study its approximated diffusion model with two thinly dependent classes of insurance businesses. Using a method of quasi-variational inequalities, we show that the optimal reinsurance follows a two-dimensional excess-of-loss reinsurance strategy, and, the optimal dividend strategy turns out to be an impulse dividend strategy with an upper and a lower barrier, i.e., every thing above the lower barrier is paid as dividends each time the surplus is above the upper barrier, otherwise no dividends are paid. Closed-form expression for the value function associated with the optimal dividend and reinsurance strategy is also given. In addition, some numerical examples are presented to illustrate the optimality results.

中文翻译：

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细化结构下交易成本和税收的最优再保险和分红

在本文中，我们研究了在 Cramer-Lundberg 风险模型下的分红和再保险最优策略问题，该模型嵌入了 Wang 和 Yuen (2005) 首次引入的稀疏依赖结构，受制于最大化预期的最优准则。累积支付的贴现股息直至破产。为了增强最优红利和再保险问题的实际相关性，考虑了非廉价再保险并对红利征收交易成本和税收，这将我们的优化问题转化为混合经典脉冲控制问题。为了更好的数学易处理性和我们控制问题的简洁、明确的解决方案，我们研究了它的近似扩散模型，而不是 Cramer-Lundberg 框架，其中包含两个弱依赖类别的保险业务。使用拟变分不等式的方法，我们证明了最优再保险遵循二维超额损失再保险策略，并且最优分红策略被证明是具有上限和下限的脉冲分红策略，即，每次盈余高于上限时，高于下限的每件事都作为红利支付，否则不支付红利。还给出了与最优分红和再保险策略相关的价值函数的闭式表达式。此外，还给出了一些数值例子来说明优化结果。最优分红策略是一个有上限和下限的冲动分红策略，即每次盈余高于上限时，下限以上的所有东西都作为红利支付，否则不支付红利。还给出了与最优分红和再保险策略相关的价值函数的闭式表达式。此外，还给出了一些数值例子来说明优化结果。最优分红策略是一个有上限和下限的冲动分红策略，即每次盈余高于上限时，下限以上的所有东西都作为红利支付，否则不支付红利。还给出了与最优分红和再保险策略相关的价值函数的闭式表达式。此外，还给出了一些数值例子来说明优化结果。