Continuous time portfolio choice under monotone preferences with quadratic penalty - stochastic interest rate case

TL;DR

This paper extends continuous-time portfolio optimization under monotone preferences with quadratic penalty to markets with stochastic interest rates, formulating it as a stochastic differential game and solving via Hamilton-Jacobi-Bellman-Isaacs equations.

Contribution

It introduces a novel approach to portfolio choice with monotone preferences in stochastic interest rate environments using game-theoretic methods.

Findings

Derived explicit optimal investment strategies.

Established the value function for the stochastic interest rate case.

Extended previous models to more realistic market conditions.

Abstract

This is a follow up of our previous paper - Trybu{\l}a and Zawisza \cite{TryZaw}, where we considered a modification of a monotone mean-variance functional in continuous time in stochastic factor model. In this article we address the problem of optimizing the mentioned functional in a market with a stochastic interest rate. We formulate it as a stochastic differential game problem and use Hamilton-Jacobi-Bellman-Isaacs equations to derive the optimal investment strategy and the value function.