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Rate of convergence for the discrete-time approximation of reflected BSDEs arising in switching problems

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  • Chassagneux, Jean-François
  • Richou, Adrien

Abstract

In this paper, we prove new convergence results improving the ones by Chassagneux et al. (2012) for the discrete-time approximation of multidimensional obliquely reflected BSDEs. These BSDEs, arising in the study of switching problems, were considered by Hu and Tang (2010) and generalized by Hamadène and Zhang (2010) and Chassagneux et al. (2011). Our main result is a rate of convergence obtained in the Lipschitz setting and under the same structural conditions on the generator as the one required for the existence and uniqueness of a solution to the obliquely reflected BSDE.

Suggested Citation

  • Chassagneux, Jean-François & Richou, Adrien, 2019. "Rate of convergence for the discrete-time approximation of reflected BSDEs arising in switching problems," Stochastic Processes and their Applications, Elsevier, vol. 129(11), pages 4597-4637.
  • Handle: RePEc:eee:spapps:v:129:y:2019:i:11:p:4597-4637
    DOI: 10.1016/j.spa.2018.12.009
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    1. repec:dau:papers:123456789/5733 is not listed on IDEAS
    2. 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.
    3. Rene Carmona & Michael Ludkovski, 2008. "Pricing Asset Scheduling Flexibility using Optimal Switching," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(5-6), pages 405-447.
    4. Hamadène, Said & Zhang, Jianfeng, 2010. "Switching problem and related system of reflected backward SDEs," Stochastic Processes and their Applications, Elsevier, vol. 120(4), pages 403-426, April.
    5. 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.
    6. 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.
    7. P. E. Kloeden & Eckhard Platen, 1992. "Higher-order implicit strong numerical schemes for stochastic differential equations," Published Paper Series 1992-1, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    8. 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.
    9. Briand, Ph. & Delyon, B. & Hu, Y. & Pardoux, E. & Stoica, L., 2003. "Lp solutions of backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 108(1), pages 109-129, November.
    10. Said Hamadène & Monique Jeanblanc, 2007. "On the Starting and Stopping Problem: Application in Reversible Investments," Mathematics of Operations Research, INFORMS, vol. 32(1), pages 182-192, February.
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    Cited by:

    1. Erhan Bayraktar & Qi Feng & Zhaoyu Zhang, 2022. "Deep Signature Algorithm for Multi-dimensional Path-Dependent Options," Papers 2211.11691, arXiv.org, revised Jan 2024.

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