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

Date

2026-01-01

Author

YILMAZ, FİKRİYE NURAY
Aydın, Elif
Temoçin, Büşra Zeynep
ALTINTAN, DERYA

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

76
views

0
downloads

Cite This

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.

Subject Keywords

Merton's jump diffusion, pure jump model, Runge-Kutta method, stochastic control, strong convergence

URI

https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=105030955604&origin=inward
https://hdl.handle.net/11511/118865

Collections

Graduate School of Applied Mathematics, Article