Strong Order Runge‐Kutta Method for Stochastic Optimal Control Problems of the Merton Jump Diffusion Model

ABSTRACT This paper studies stochastic Runge‐Kutta (SRK) approximation for solving stochastic optimal control problems where the state process is governed by Merton's jump‐diffusion model. We propose a practical numerical scheme based on the SRK method to approximate the solutions of the resulting equations. Moreover, strong order conditions of the proposed scheme are provided. Following the presentation of the main scheme of Merton's optimal consumption‐investment problem, solution of a controlled pure jump model is introduced as a variant. Numerical experiments demonstrate the efficiency of the SRK method in solving the optimal consumption‐investment problem, highlighting its potential for practical applications in financial decision‐making under discontinuous dynamics.