We consider a diffusion approximation to an insurance risk model where an external driver models a stochastic environment. The insurer can buy reinsurance. Moreover, it is possible to invest in a financial market that depends on the insurance market. The financial market is also driven by the environmental process. Our goal is to maximise terminal expected utility. In particular, we consider the case of SAHARA utility functions. In the case of proportional and excess-of-loss reinsurance, we obtain explicit results.

中文翻译：

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扩散模型中的最优再保险和投资

我们考虑对保险风险模型的扩散近似，其中外部驱动因素对随机环境进行建模。保险人可以购买再保险。此外，有可能在依赖保险市场的金融市场上进行投资。金融市场也受到环境过程的驱动。我们的目标是最大化终端的预期效用。特别地，我们考虑SAHARA实用程序功能的情况。在比例和超额损失再保险的情况下，我们获得了明确的结果。