Non-negativity preserving numerical algorithms for stochastic differential equations

2005/09/30 by Esteban Moro, Moro, Esteban, Henri Schurz +1
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #60H10 #60H15 #65C30 #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Probability (math.PR) #Stochastic processes and financial applications #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.math/0509724

openalex publication_date 2005/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations
• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States

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