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Quantitative stability and numerical analysis of Markovian quadratic BSDEs with reflection

The authors thank the editor and both referees for their careful reading and helpful comments. Dingqian Sun is partially supported by China Scholarship Council. Gechun Liang is partially supported by the National Natural Science Foundation of China (Grant No. 12171169) and Guangdong Basic and Applied Basic Research Foundation(Grant No. 2019A1515011338). GL thanks J. F. Chassagneux and A. Richou for helpful and inspiring discussions on how to extend to the state dependent volatility case. Shanjian Tang is partially supported by National Science Foundation of China (Grant No. 11631004) and National Key R&D Program of China (Grant No. 2018YFA0703903).

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  • Mathematics Subject Classification: 65C30, 60H10, 60H30.

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  • [1]

    Bayraktar, E. and Yao, S., Quadratic reflected BSDEs with unbounded obstacles, Stochastic Processes and their Applications, 2012, 122(4): 1155−1203.

    doi: 10.1016/j.spa.2011.12.013.

    [2]

    Bouchard, B. and Chassagneux, J. F., Discrete-time approximation for continuously and discretely reflected BSDEs, Stochastic Processes and their Applications, 2008, 118(12): 2269−2293.

    doi: 10.1016/j.spa.2007.12.007.

    [3]

    Bouchard, B. and Touzi, N., Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations, Stochastic Processes and their Applications, 2004, 111(2): 175−206.

    doi: 10.1016/j.spa.2004.01.001.

    [4]

    Briand, P. and Hu, Y., BSDE with quadratic growth and unbounded terminal value, Probability Theory and Related Fields, 2006, 136(4): 604−618.

    doi: 10.1007/s00440-006-0497-0.

    [5]

    Briand, P. and Hu, Y., Quadratic BSDEs with convex generators and unbounded terminal conditions, Probability Theory and Related Fields, 2008, 141(3/4): 543−567.

    [6]

    Chassagneux, J. F. and Richou, A., Numerical simulation of quadratic BSDEs, The Annals of Applied Probability, 2016, 26(1): 262−304.

    [7]

    Gobet, E., Lemor, J. P. and Warin, X., A regression-based Monte Carlo method to solve backward stochastic differential equations, The Annals of Applied Probability, 2005, 15(3): 2172−2202.

    [8]

    Hu, Y., Li, X. and Wen, J., Anticipated backward stochastic differential equations with quadratic growth, Journal of Differential Equations, 2021, 270: 1298−1331.

    doi: 10.1016/j.jde.2020.07.001.

    [9]

    Imkeller, P. and Dos Reis, G., Path regularity and explicit convergence rate for BSDE with truncated quadratic growth, Stochastic Processes and their Applications, 2010, 120(3): 348−379.

    doi: 10.1016/j.spa.2009.11.004.

    [10]

    El Karoui, N., Kapoudjian, C., Pardoux, E., Peng, S. and Quenez, M. C., Reflected solutions of backward SDE’s, and related obstacle problems for PDE’s, The Annals of Probability, 1997, 25(2): 702−737.

    [11] Lepeltier, J. P. and Xu, M., Reflected BSDE with quadratic growth and unbounded terminal value, arXiv: 0711.0619v1, 2007.
    [12] Kazamaki, N., Continuous Exponential Martingales and BMO, Lecture Notes in Mathematics, Springer, Berlin, Heidelberg, 1994.
    [13] Kloeden, P. E. and Platen, E., Numerical Solution of Stochastic Differential Equations, Applications of Mathematics, Springer, Berlin, 1992.
    [14]

    Kobylanski, M., Backward stochastic differential equations and partial differential equations with quadratic growth, The Annals of Probability, 2000, 28(2): 558−602.

    [15]

    Kobylanski, M., Lepeltier, J. P., Quenez, M. C. and Torres, S., Reflected BSDE with superlinear quadratic coefficient, Probability and Mathematical Statistics, 2002, 22(1): 51−83.

    [16]

    Ma, J. and Zhang, J., Representations and regularities for solutions to BSDEs with reflections, Stochastic Processes and their Applications, 2005, 115(4): 539−569.

    doi: 10.1016/j.spa.2004.05.010.

    [17]

    Richou, A., Numerical simulation of BSDEs with drivers of quadratic growth, The Annals of Applied Probability, 2011, 21(5): 1933−1964.

    [18]

    Sun, D. Q., The convergence rate from discrete to continuous optimal investment stopping problem, Chinese Annals of Mathematics, Series B, 2021, 42(2): 259−280.

    doi: 10.1007/s11401-021-0256-7.

    [19]

    Zhang, J., A numerical scheme for BSDEs, The Annals of Applied Probability, 2004, 14(1): 459−488.

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