  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.
