A new numerical scheme for stochastic control problems of jump-diffusion equations by means of Runge-Kutta method

ALTINTAN, DERYA; Aydin, Elif; YILMAZ, FİKRİYE; TEMOÇİN, BÜŞRA

doi:10.1016/j.cam.2026.117862

A new numerical scheme for stochastic control problems of jump-diffusion equations by means of Runge-Kutta method

ALTINTAN D., Aydin E., YILMAZ F. N., TEMOÇİN B. Z.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, vol.489, 2027 (SCI-Expanded, Scopus)

Publication Type: Article / Article
Volume: 489
Publication Date: 2027
Doi Number: 10.1016/j.cam.2026.117862
Journal Name: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Applied Science & Technology Source, Compendex, INSPEC, MathSciNet, zbMATH, Academic Search Ultimate (EBSCO), Engineering Source (EBSCO)
Middle East Technical University Affiliated: Yes

Abstract

In this paper, a new numerical scheme for optimal control of jump-diffusion model is proposed by using stohastic Runge-Kutta (SRK) method. After discretizing the problem with the SRK method, optimality conditions are obtained by using the discretize-then-optimize approach. It is shown that the constructed numerical scheme is similar to the continuous optimality conditions obtained by using the Hamilton-Jacobi-Bellman equations. Moreover, a numerical scheme for control problems of Ornstein-Uhlenbeck (OU) with jump is presented as a simple version of jump diffusion equations. Some numerical examples are chosen to show the efficiency of the theoretical results.