Non-negativity preserving numerical algorithms for stochastic differential equations

TL;DR

This paper develops and analyzes splitting-step numerical algorithms that preserve non-negativity for solving Ito-type stochastic differential equations, with applications in finance, biology, and physics.

Contribution

It introduces a new splitting-step algorithm with proven convergence and demonstrates its effectiveness across various stochastic models.

Findings

Convergence of the new splitting-step method is established.

Numerical experiments show accurate preservation of non-negativity.

Applications include finance, measure-valued diffusions, and superBrownian motion.

Abstract

Construction of splitting-step methods and properties of related non-negativity and boundary preserving numerical algorithms for solving stochastic differential equations (SDEs) of Ito-type are discussed. We present convergence proofs for a newly designed splitting-step algorithm and simulation studies for numerous numerical examples ranging from stochastic dynamics occurring in asset pricing theory in mathematical finance (SDEs of CIR and CEV models) to measure-valued diffusion and superBrownian motion (SPDEs) as met in biology and physics.