Optimal investment with insurable background risk and nonlinear portfolio allocation frictions

Hugo E. Ramírez and Rafael Serrano ()

Applied Mathematics and Computation, 2025, vol. 485, issue C

Abstract: 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.

Keywords: Portfolio allocation; Insurance demand; Background risk; Jump-diffusions; CRRA utility; Hamilton-Jacobi-Bellman equation; Differential rates; Separation theorem (search for similar items in EconPapers)
Date: 2025
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Related works:
Working Paper: Optimal investment with insurable background risk and nonlinear portfolio allocation frictions (2023)
Working Paper: Optimal investment with insurable background risk and nonlinear portfolio allocation frictions (2023)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:485:y:2025:i:c:s0096300324004843

DOI: 10.1016/j.amc.2024.129023

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