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A Multi-Step Algorithm for BSDEs Based On a Predictor-Corrector Scheme and Least-Squares Monte Carlo

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  • Qiang Han

    (Shandong University)

  • Shaolin Ji

    (Shandong University)

Abstract

We design a multi-step predictor-corrector scheme for backward stochastic differential equations (BSDEs). This scheme tries its best to retain the simplicity and improve its convergence rate as much as possible. We investigate the stability and rigorously deduce the error estimates of this scheme. Numerical experiments are compared with the scheme given by Gobet et al. (Math Comput, 85(299): 1359-1391, 2016a) and are given to illustrate that the multi-step predictor-corrector scheme is an efficient probabilistic numerical method.

Suggested Citation

  • Qiang Han & Shaolin Ji, 2022. "A Multi-Step Algorithm for BSDEs Based On a Predictor-Corrector Scheme and Least-Squares Monte Carlo," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2403-2426, December.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:4:d:10.1007_s11009-022-09943-4
    DOI: 10.1007/s11009-022-09943-4
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    References listed on IDEAS

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    1. Bouchard, Bruno & Touzi, Nizar, 2004. "Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 111(2), pages 175-206, June.
    2. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    3. Bender, Christian & Denk, Robert, 2007. "A forward scheme for backward SDEs," Stochastic Processes and their Applications, Elsevier, vol. 117(12), pages 1793-1812, December.
    4. Vlad Bally & Gilles Pagès & Jacques Printems, 2005. "A Quantization Tree Method For Pricing And Hedging Multidimensional American Options," Mathematical Finance, Wiley Blackwell, vol. 15(1), pages 119-168, January.
    5. repec:dau:papers:123456789/5522 is not listed on IDEAS
    6. Crisan, D. & Manolarakis, K. & Touzi, N., 2010. "On the Monte Carlo simulation of BSDEs: An improvement on the Malliavin weights," Stochastic Processes and their Applications, Elsevier, vol. 120(7), pages 1133-1158, July.
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