In this paper we consider an optimal investment and reinsurance problem with partially unknown model parameters which are allowed to be learned. The model includes multiple business lines and dependence between them. The aim is to maximize the expected exponential utility of terminal wealth which is shown to imply a robust approach. We can solve this problem using a generalized HJB equation where derivatives are replaced by generalized Clarke gradients. The optimal investment strategy can be determined explicitly and the optimal reinsurance strategy is given in terms of the solution of an equation. Since this equation is hard to solve, we derive bounds for the optimal reinsurance strategy via comparison arguments.

中文翻译：

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稳健的最优投资和学习再保险问题

在本文中，我们考虑了一个最优投资和再保险问题，其中允许学习部分未知的模型参数。该模型包括多个业务线以及它们之间的依赖关系。目的是最大化终端财富的预期指数效用，这表明这是一种稳健的方法。我们可以使用广义 HJB 方程解决这个问题，其中导数被广义克拉克梯度代替。最优投资策略可以明确确定，最优再保险策略可以通过方程的解来给出。由于这个方程很难求解，我们通过比较参数推导出最优再保险策略的界限。