On construction of boundary preserving numerical schemes

TL;DR

This paper introduces a novel numerical scheme that combines semi-discrete and split-step methods to preserve boundary conditions, specifically positivity, in models like Ait-Sahalia.

Contribution

It develops an explicit, positivity-preserving numerical scheme by integrating semi-discrete and split-step techniques for stochastic models.

Findings

Successfully applied to the Ait-Sahalia model

Preserves positivity of solutions

Offers an explicit computational method

Abstract

Our aim in this note is to extend the semi discrete technique by combine it with the split step method. We apply our new method to the Ait-Sahalia model and propose an explicit and positivity preserving numerical scheme.