Exact Simulation of One-dimensional Stochastic Differential Equations involving the local time at zero of the unknown process

2011/02/13 by Pierre Étoré, Pierre Etore, Etore, Pierre +3 · 1 citation
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR

paper · pdf · doi:10.48550/arxiv.1102.2565

21 pages références comprises

openalex publication_date 2011/02/13 · arxiv created 2013/01/14 · arxiv updated 2013/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we extend the exact simulation methods of Beskos et al. to the solutions of one-dimensional stochastic differential equations involving the local time of the unknown process at point zero. In order to perform the method we compute the law of the skew Brownian motion with drift. The method presented in this article covers the case where the solution of the SDE with local time corresponds to a divergence form operator with a discontinuous coefficient at zero. Numerical examples are shown to illustrate the method and the performances are compared with more traditional discretization schemes.

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