Continuous time portfolio choice under monotone preferences with quadratic penalty - stochastic interest rate case (1404.5408v1)

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.