Existence, uniqueness, and approximation of solutions of jump-diffusion SDEs with discontinuous drift

TL;DR

This paper investigates jump-diffusion SDEs with discontinuous drift, establishing existence, uniqueness, and convergence rates of numerical schemes, with applications in energy market control problems.

Contribution

It provides new theoretical results on the existence, uniqueness, and numerical approximation of jump-diffusion SDEs with discontinuous drift.

Findings

Proves existence and uniqueness of strong solutions.

Establishes the Euler-Maruyama scheme's convergence rate as 1/2.

Applicable to energy market optimal control problems.

Abstract

In this paper we study jump-diffusion stochastic differential equations (SDEs) with a discontinuous drift coefficient and a possibly degenerate diffusion coefficient. Such SDEs appear in applications such as optimal control problems in energy markets. We prove existence and uniqueness of strong solutions. In addition we study the strong convergence order of the Euler-Maruyama scheme and recover the optimal rate $1/2$.