MP and DPP for Mean-Variance Portfolio Selection Problem with Poisson Jumps, Recursive Utility and Their Relationship

TL;DR

This paper addresses the mean-variance portfolio selection problem incorporating Poisson jumps and recursive utility, deriving optimal portfolios and efficient frontiers using maximum principle and dynamic programming, and comparing jump and no-jump scenarios.

Contribution

It introduces a novel analysis of the mean-variance problem with Poisson jumps using both maximum principle and dynamic programming, and explores their relationship.

Findings

Derived optimal portfolios considering Poisson jumps.

Compared efficient frontiers with and without jumps.

Established the relationship between solution methods.

Abstract

In this paper, the mean-variance portfolio selection problem with Poisson jumps are studied, where the recursive utility is given by the solution to a backward stochastic differential equation with Poisson jumps. Both the maximum principle and dynamic programming principle are applied to solve this problem, and their relationship is also investigated. The optimal portfolio and efficient frontier of Markowitz's type are derived using both methods. A comparison of efficient frontiers obtained in this paper and in the framework without jumps is conducted.