This paper investigates time-consistent reinsurance(excess-of-loss, proportional) and investment strategies for an ambiguity averse insurer(abbr. AAI). The AAI is ambiguous towards the insurance and financial markets. In the AAI's attitude, the intensity of the insurance claims' number and the market price of risk of a stock can not be estimated accurately. This formulation of ambiguity is similar to the uncertainty of different equivalent probability measures. The AAI can purchase excess-of-loss or proportional reinsurance to hedge the insurance risk and invest in a financial market with cash and an ambiguous stock. We investigate the optimization goal under smooth ambiguity given in Klibanoff, P., Marinacci, M., & Mukerji, S. [(2005). A smooth model of decision making under ambiguity. Econometrica 73, 1849–1892], which aims to search the optimal strategies under average case. The utility function does not satisfy the Bellman's principle and we employ the extended HJB equation proposed in Björk, T. & Murgoci, A. [(2014). A theory of Markovian time-inconsistent stochastic control in discrete time. Finance and Stochastics 18(3), 545–592] to solve this problem. In the end of this paper, we derive the equilibrium reinsurance and investment strategies under smooth ambiguity and present the sensitivity analysis to show the AAI's economic behaviors.

中文翻译：

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平滑模糊效用下 AAI 的时间一致性再保险和投资策略

本文研究了模糊规避保险公司（简称 AAI）的时间一致性再保险（超额损失，比例）和投资策略。AAI 对保险和金融市场含糊其辞。在AAI看来，保险索赔数量的强度和股票的风险市场价格无法准确估计。这种歧义的表述类似于不同等效概率度量的不确定性。AAI可以购买超额损失或比例再保险来对冲保险风险，用现金和不明确的股票投资金融市场。我们研究了 Klibanoff, P., Marinacci, M., & Mukerji, S. [(2005) 中给出的平滑模糊下的优化目标。歧义下的平滑决策模型。计量经济学 73, 1849–1892], 旨在搜索平均情况下的最佳策略。效用函数不满足贝尔曼原理，我们采用 Björk, T. & Murgoci, A. [(2014) 中提出的扩展 HJB 方程。离散时间中的马尔可夫时间不一致随机控制理论。Finance and Stochastics 18(3), 545–592] 来解决这个问题。在本文的最后，我们推导出了平滑模糊下的均衡再保险和投资策略，并通过敏感性分析来展示AAI的经济行为。545-592]来解决这个问题。在本文的最后，我们推导出了平滑模糊下的均衡再保险和投资策略，并通过敏感性分析来展示AAI的经济行为。545-592]来解决这个问题。在本文的最后，我们推导出了平滑模糊下的均衡再保险和投资策略，并通过敏感性分析来展示AAI的经济行为。