Adapted time steps explicit scheme for monotone BSDEs

2016/11/30 by Arnaud Lionnet, Lionnet, Arnaud · 1 citation
Economics, Econometrics and Finance · Engineering · Mathematics · #60H30 #60H35 #65C30 #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1612.00077

openalex publication_date 2016/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the numerical strong stability of explicit schemes for the numerical approximation of the solution to a BSDE where the driver has polynomial growth in the primary variable and satisfies a monotone decreasing condition, and we introduce an explicit scheme with adapted time-steps that guarantee numerical strong stability. We then prove the convergence of this scheme and illustrate it with numerical simulations.

Citations

• An explicit Euler scheme with strong rate of convergence for financial\n SDEs with non-Lipschitz coefficients
• Convergence and qualitative properties of modified explicit schemes for BSDEs with polynomial growth
• Contracting theory with competitive interacting agents

Cited by

• Strong and weak divergence of exponential and linear-implicit Euler\n approximations for stochastic partial differential equations with\n superlinearly growing nonlinearities

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• Linear multi-step schemes for BSDEs
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