论文标题
在稀疏结构下的交易成本和税收的最佳再保险和股息
Optimal reinsurance and dividends with transaction costs and taxes under thinning structure
论文作者
论文摘要
在本文中，我们调查了Cramér-Lundberg风险模型的最佳股息和再保险策略问题，该模型嵌入了稀疏依赖性结构，该结构首先由Wang and Yuen（2005）引入，但要遵守最大程度地提高预期累积的折扣股权销售股权的最佳标准。为了增强最佳股息和再保险问题的实际相关性，考虑了非廉价再保险，并将交易成本和税收征收在股息上，这将我们的优化问题转化为混合的经典型号控制问题。为了更好的数学障碍性和整洁的控制问题的明确解决方案，而不是Cramér-Lundberg框架，我们研究了其近似的扩散模型，其中有两个薄薄的保险公司类别。使用一种准变量不平等的方法，我们表明，最佳再保险遵循二维过度损坏的再保险策略，并且，最佳的最佳股息策略证明是一种冲动股息策略，上层和下障碍较低的每一个较低障碍都没有支付，否则每次派发级别的差异都在上面是上述时间。还给出了与最佳股息和再保险策略相关的价值函数的封闭式表达。另外，提出了一些数值示例，以说明最佳结果。
In this paper, we investigate the problem of optimal strategies of dividend and reinsurance under the Cramér-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 Cramér-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.
