This paper studies the closed-loop equilibrium reinsurance-investment problem with insider information and default risk. The financial market consists of one risky asset, one defaultable bond, and one risk-free asset. The surplus process is governed by a jump-diffusion process. Two kinds of dependencies between the insurance market and the financial market are considered. In addition, the insurer has some extra claims information available from the beginning of the trading interval. The objective of the insurer is to choose a time-consistent reinsurance-investment strategy so as to maximize the expected terminal wealth while minimizing the variance of the terminal wealth. Since this problem is time-inconsistent, using closed-loop control approach from the perspective of game theory, we establish the extended Hamilton–Jacobi–Bellman (HJB) equations for the postdefault case and the predefault case, respectively. Closed-form solutions for the closed-loop equilibrium reinsurance-investment strategy and the corresponding value function are obtained. Finally, we provide a series of numerical examples to illustrate the effects of insider information and other some important model parameters on the closed-loop equilibrium reinsurance and investment strategies. The result analyses reveal some interesting phenomena and provide useful guidances for reinsurance and investment in reality.

中文翻译：

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具有内幕信息和违约风险的闭环均衡再保险投资策略

本文研究了具有内幕信息和违约风险的闭环均衡再保险投资问题。金融市场由一种风险资产，一种可违约债券和一种无风险资产组成。剩余过程由跳跃扩散过程控制。考虑了保险市场和金融市场之间的两种依赖关系。此外，保险人从交易间隔开始就可获得一些额外的索赔信息。保险公司的目标是选择时间一致的再保险投资策略，以使预期的最终财富最大化，同时使最终财富的方差最小。由于此问题是时间不一致的，因此从博弈论的角度使用闭环控制方法，我们分别针对默认后情况和默认前情况建立了扩展的Hamilton–Jacobi–Bellman（HJB）方程。得到了闭环均衡再保险投资策略的闭式解和相应的价值函数。最后，我们提供了一系列数值示例来说明内部信息和其他一些重要模型参数对闭环均衡再保险和投资策略的影响。结果分析揭示了一些有趣的现象，并为现实中的再保险和投资提供了有用的指导。我们提供了一系列数值示例来说明内部信息和其他一些重要模型参数对闭环均衡再保险和投资策略的影响。结果分析揭示了一些有趣的现象，并为现实中的再保险和投资提供了有用的指导。我们提供了一系列数值示例来说明内部信息和其他一些重要模型参数对闭环均衡再保险和投资策略的影响。结果分析揭示了一些有趣的现象，并为现实中的再保险和投资提供了有用的指导。