Stochastic differential portfolio games with Duffie-Kan interest rate

Purpose - The purpose of this paper is to research stochastic dynamic investment games with stochastic interest rate model in continuous time between two investors. The market interest rate has the dynamics of Duffie-Kan interest rate. Design/methodology/approach - Recently, there has been an increasing interest in financial market models whose key parameters, such as the bank interest rate, stocks appreciation rates, and volatility rates, are modulated by stochastic interest rate. This paper uses the Duffie-Kan stochastic interest rate model to develop stochastic differential portfolio games. By the HJB optimality equation, a general result in optimal control for a stochastic differential game with a general utility payoff function is obtained. Findings - Derive a general result in optimal control for a stochastic differential game with a general utility payoff function. The explicit optimal strategies and value of the games are obtained for the constant relative risk aversion utility games of fixed duration. Research limitations/implications - Accessibility and availability of stochastic interest rate data are the main limitations, which apply. Practical implications - The results obtained in this paper could be used as a guide to actual portfolio games. Originality/value - This paper presents a new approach for the optimal portfolio model under compound jump processes. The paper is aimed at actual portfolio games.