In this article , we propose a new numerical computation scheme for Markovian backward stochastic differential equations (BSDEs ) by connecting the semi-analytic short-term approximation applied to each time interval, which has a very simple form to implement. We give the error analysis for BSDEs which have generators of quadratic growth with respect to the control variables and bounded terminal conditions. Although the scheme requires higher regularities than the standard method , one can avoid altogether time-consuming Monte Carlo simulation or other numerical integration for estimating conditional expectations at each space-time node. We provide numerical examples of quadratic-growth (qg) BSDEs as well as standard Lipschitz BSDEs to illustrate the proposed scheme and its empirical convergence rate .
This article proposes a new approximation scheme for quadratic-growth BSDEs in a Markovian setting by connecting a series of semi-analytic asymptotic expansions applied to short-time intervals. Although there remains a condition which needs to be checked a posteriori , one can avoid altogether time-consuming Monte Carlo simulation and other numerical integrations for estimating conditional expectations at each space-time node. Numerical examples of quadratic-growth as well as Lipschitz BSDEs suggest that the scheme works well even for large quadratic coefficients, and a fortiori for large Lipschitz constants .
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In this article , we propose a new numerical computation scheme for Markovian backward stochastic differential equations (BSDEs ) by connecting the
This article proposes a new approximation scheme for quadratic-growth BSDEs in a Markovian setting by connecting a series of
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short-term approximation applied to each time interval, which has a very simple form to implement. We give the error analysis for BSDEs which have generators of quadratic growth with respect to the control variables and bounded terminal conditions. Although the scheme requires higher regularities than the standard method
asymptotic expansions applied to short-time intervals. Although there remains a condition which needs to be checked a posteriori
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or other numerical integration
and other numerical integrations
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We provide numerical
Numerical
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(qg) BSDEs
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standard Lipschitz BSDEs to illustrate the proposed scheme and its empirical convergence rate
Lipschitz BSDEs suggest that the scheme works well even for large quadratic coefficients, and a fortiori for large Lipschitz constants