A Monte Carlo method for backward stochastic differential equations with Hermite martingales

Antoon Pelsser and Gnameho Kossi ()
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Gnameho Kossi: Deptartment of Quantitative Economics, Maastricht University, Maastricht, Netherlands

Monte Carlo Methods and Applications, 2019, vol. 25, issue 1, 37-60

Abstract: Backward stochastic differential equations (BSDEs) appear in many problems in stochastic optimal control theory, mathematical finance, insurance and economics. This work deals with the numerical approximation of the class of Markovian BSDEs where the terminal condition is a functional of a Brownian motion. Using Hermite martingales, we show that the problem of solving a BSDE is identical to solving a countable infinite-dimensional system of ordinary differential equations (ODEs). The family of ODEs belongs to the class of stiff ODEs, where the associated functional is one-sided Lipschitz. On this basis, we derive a numerical scheme and provide numerical applications.

Keywords: Regression; BSDE; ODE; Hermite polynomials; martingale (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1515/mcma-2019-2028

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