Two Stochastic Control Methods for Mean-Variance Portfolio Selection of Jump Diffusions and Their Relationship

TL;DR

This paper compares the maximum principle and dynamic programming approaches for mean-variance portfolio optimization in jump diffusion models, revealing their connections and deriving optimal portfolios and efficient frontiers.

Contribution

It provides a detailed analysis of the relationship between two control methods in jump diffusion portfolio optimization, including explicit connections between adjoint processes and value functions.

Findings

Optimal portfolios and efficient frontiers derived by both methods.

Established connections between adjoint processes and value functions.

Enhanced understanding of control methods in jump diffusion models.

Abstract

This paper is concerned with the maximum principle and dynamic programming principle for mean-variance portfolio selection of jump diffusions and their relationship. First, the optimal portfolio and efficient frontier of the problem are obtained using both methods. Furthermore, the relationship between these two methods is investigated. Specially, the connections between the adjoint processes and value function are given.