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Finite Difference Methods for the BSDEs in Finance

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  • Guangbao Guo

    (Department of Statistics, Shandong University of Technology, Zibo 255000, China)

Abstract

This paper gives a review of numerical methods for solving the BSDEs, especially, finite difference methods. For numerical methods of finite difference, we should divide them into three branches. Distributed method (or parallel method) should now become a hot topic. It is a key reason we present the review. We give a brief survey on the financial problems. The problems include solution and simulation methods for the BSDEs. We first describe the BSDEs, and then outline the main techniques and main results of the BSDEs. In addition, we compare with the errors between these methods and the Euler method on the BSDEs.

Suggested Citation

  • Guangbao Guo, 2018. "Finite Difference Methods for the BSDEs in Finance," IJFS, MDPI, vol. 6(1), pages 1-15, March.
    • Handle: RePEc:gam:jijfss:v:6:y:2018:i:1:p:26-:d:134745
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    References listed on IDEAS

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    1. repec:dau:papers:123456789/5733 is not listed on IDEAS
    2. Bouchard, Bruno & Chassagneux, Jean-François, 2008. "Discrete-time approximation for continuously and discretely reflected BSDEs," Stochastic Processes and their Applications, Elsevier, vol. 118(12), pages 2269-2293, December.
    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. Richard Rouge & Nicole El Karoui, 2000. "Pricing Via Utility Maximization and Entropy," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 259-276, April.
    5. Gobet, Emmanuel & Labart, Céline, 2007. "Error expansion for the discretization of backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 117(7), pages 803-829, July.
    6. Elie, Romuald & Kharroubi, Idris, 2010. "Probabilistic representation and approximation for coupled systems of variational inequalities," Statistics & Probability Letters, Elsevier, vol. 80(17-18), pages 1388-1396, September.
    7. Fabio Antonelli & Andrea Pascucci, 2005. "On the viscosity solutions of a stochastic differential utility problem," Finance 0503021, University Library of Munich, Germany.
    8. Bouchard, Bruno & Elie, Romuald, 2008. "Discrete-time approximation of decoupled Forward-Backward SDE with jumps," Stochastic Processes and their Applications, Elsevier, vol. 118(1), pages 53-75, January.
    9. Rong, Situ, 1997. "On solutions of backward stochastic differential equations with jumps and applications," Stochastic Processes and their Applications, Elsevier, vol. 66(2), pages 209-236, March.
    10. repec:dau:papers:123456789/5522 is not listed on IDEAS
    11. 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.
    12. 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.
    13. Ma, Jin & Zhang, Jianfeng, 2005. "Representations and regularities for solutions to BSDEs with reflections," Stochastic Processes and their Applications, Elsevier, vol. 115(4), pages 539-569, April.
    14. Royer, Manuela, 2006. "Backward stochastic differential equations with jumps and related non-linear expectations," Stochastic Processes and their Applications, Elsevier, vol. 116(10), pages 1358-1376, October.
    15. 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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    Cited by:

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