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This article proposes a new approximation scheme for quadratic-growth BSDEsin a Markovian setting by connecting a series of semi-analytic asymptoticexpansions applied to short-time intervals. Although there remains a conditionwhich needs to be checked a posteriori, one can avoid altogether time-consumingMonte Carlo simulation and other numerical integrations for estimatingconditional expectations at each space-time node. Numerical examples ofquadratic-growth as well as Lipschitz BSDEs suggest that the scheme works welleven for large quadratic coefficients, and a fortiori for large Lipschitzconstants.

Solving Backward Stochastic Differential Equations with quadratic-growth drivers by Connecting the Short-term Expansions