# Lower error bounds and optimality of approximation for jump-diffusion SDEs with discontinuous drift

## TL;DR

This paper proves lower error bounds for numerical methods solving jump-diffusion equations with discontinuous drift and shows a specific method is optimal.

## Contribution

The paper establishes sharp lower error bounds and proves the optimality of a transformation-based quasi-Milstein scheme for jump-diffusion SDEs.

## Key findings

- Lower error bounds of order 3/4 are proven for non-adaptive and jump-adapted schemes.
- The transformation-based jump-adapted quasi-Milstein scheme is shown to be optimal.
- Discontinuous drift in jump-diffusion SDEs is effectively analyzed with these bounds.

## Abstract

In this paper sharp lower error bounds for numerical methods for jump-diffusion stochastic differential equations (SDEs) with discontinuous drift are proven. The approximation of jump-diffusion SDEs with non-adaptive as well as jump-adapted approximation schemes is studied and lower error bounds of order 3/4 for both classes of approximation schemes are provided. This yields optimality of the transformation-based jump-adapted quasi-Milstein scheme.