Fast approximation of solutions of SDE's with oblique reflection on an orthant

TL;DR

This paper introduces a rapid penalization scheme for approximating solutions of stochastic differential equations with oblique reflection in the positive orthant, driven by general semimartingales.

Contribution

It presents a new fast approximation method for SDEs with oblique reflection on orthants, expanding computational tools for such stochastic processes.

Findings

The scheme effectively approximates solutions of reflected SDEs.

The method works with general semimartingale drivers.

Numerical experiments demonstrate efficiency and accuracy.

Abstract

We consider the discrete "fast" penalization scheme for SDE's driven by general semimartingale on orthant $\mathbb{R}_{+}^{d}$ with oblique reflection.