Abstract

In this article, we study the optimal investment and reinsurance problem involving a defaultable security for a group which holds shares of both an insurance company and a reinsurance company. Assuming that the claim process is described by a Brownian motion with drift, and the insurer can purchase proportional reinsurance and invest in a financial market consisting of a risk-free asset, a risky asset and a defaultable bond. Moreover, the reinsurer is allowed to invest in a risk-free asset and a stock. With both the insurer and the reinsurer taken into account, the group aims to maximize the expected exponential utility of the weighted sum of the insurer’s and the reinsurer’s terminal wealth. By using the dynamic programming approach, we study the pre-default case and post-default case, respectively. In both cases, the closed-form expressions for the optimal strategies and the corresponding value functions are derived. Finally, numerical examples are given to illustrate the effects of model parameters on the optimal strategies.

摘要

在本文中，我们研究了同时持有保险公司和再保险公司股份的集团的违约证券的最优投资和再保险问题。假设索赔过程是由具有漂移的布朗运动描述的，则保险公司可以购买比例再保险，并投资于由无风险资产，风险资产和可违约债券组成的金融市场。此外，再保险公司可以投资无风险资产和股票。考虑到保险人和再保险人，该小组的目标是使保险人和再保险人的最终财富加权总和的预期指数效用最大化。通过使用动态编程方法，我们分别研究了默认情况和默认情况。在这两种情况下 推导了最优策略的闭式表达式和相应的价值函数。最后，通过数值例子说明了模型参数对最优策略的影响。