A new numerical scheme for stochastic control problems of jump-diffusion equations by means of Runge-Kutta method
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, cilt.489, 2027 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 489
- Basım Tarihi: 2027
- Doi Numarası: 10.1016/j.cam.2026.117862
- Dergi Adı: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Applied Science & Technology Source, Compendex, INSPEC, MathSciNet, zbMATH, Academic Search Ultimate (EBSCO), Engineering Source (EBSCO)
- Gazi Üniversitesi Adresli: Evet
Özet
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.