We study optimal investment and insurance demand in a continuous-time model that combines risky assets with an insurable background risk. This risk takes the form of a jump-diffusion process that reduces the return rate of the agent's wealth. The main distinctive feature of our model is that the agent's decision on portfolio choice and insurance demand causes nonlinear friction in the dynamics of the wealth process. We use the HJB equation to find the optimal conditions for the agent to fully, partially, or totally insure against the background risk. We consider different types of friction, such as differential borrowing and lending rates. We also show a mutual-fund separation result and provide numerical examples.

中文翻译：

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具有可保背景风险和非线性投资组合配置摩擦的最优投资


我们在连续时间模型中研究最优投资和保险需求，该模型将风险资产与可保背景风险相结合。这种风险表现为跳跃扩散过程，降低了代理人财富的回报率。我们模型的主要显着特征是，代理人对投资组合选择和保险需求的决策会导致财富过程动态中的非线性摩擦。我们使用 HJB 方程来找到代理完全、部分或完全防范背景风险的最佳条件。我们考虑不同类型的摩擦，例如不同的借贷利率。我们还展示了共同基金分离结果并提供了数值示例。