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Optimal investment with insurable background risk and nonlinear portfolio allocation frictions

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  • Ramírez, H
  • Serrano, R

Abstract

We study investment and insurance demand decisions for an agent in a theoretical continuoustime expected utility maximization model that combines risky assets with an (exogenous) insurable background risk. This risk takes the form of a jump-diffusion process with negative jumps in the return rate of the (self-financed) 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 dynamic programming approach to find optimality conditions under which the agent assumes the insurable risk entirely, or partially, or purchases total insurance against it. In particular, we consider differential and piece-wise linear portfolio allocation frictions, with differential borrowing and lending rates as our most emblematic example. Finally, we present a mutual-fund separation result and illustrate our results with several numerical examples when the adverse jump risk has Beta distribution.

Suggested Citation

  • Ramírez, H & Serrano, R, 2023. "Optimal investment with insurable background risk and nonlinear portfolio allocation frictions," Documentos de Trabajo 20658, Universidad del Rosario.
    • Handle: RePEc:col:000092:020658
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    Keywords

    Portfolio allocation; Insurance demand; CRRA utility; Background risk; Jump-diffusions; Dynamic programming; Differential rates; Fund separation Theorem;
    All these keywords.

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