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A regression-based Monte Carlo method to solve two-dimensional forward backward stochastic differential equations. (English) Zbl 1494.65005

MSC:

65C30 Numerical solutions to stochastic differential and integral equations
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
65C05 Monte Carlo methods
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References:

[1] Pardoux, E.; Peng, S. G., Backward stochastic differential equations and quasilinear parabolic partial differential equations, Stochastic Partial Differential Equations and Their Applications, 200-217 (1992), Berlin: Springer, Berlin · Zbl 0766.60079 · doi:10.1007/BFb0007334
[2] Zhang, G.; Gunzburger, M.; Zhao, W., A sparse-grid method for multi-dimensional backward stochastic differential equations, J. Comput. Math., 31, 221-248 (2013) · Zbl 1289.65011 · doi:10.4208/jcm.1212-m4014
[3] Fu, Y.; Zhao, W.; Zhou, T., Efficient spectral sparse grid approximations for solving multi-dimensional forward backward SDEs, Discrete Contin. Dyn. Syst., Ser. B, 22, 3439-3458 (2017) · Zbl 1368.60071
[4] Ding, D.; U, S. C., Efficient option pricing methods based on Fourier series expansions, J. Math. Res. Expo., 31, 12-22 (2011) · Zbl 1237.62146
[5] Fang, F.; Oosterlee, C. W., Pricing early-exercise and discrete barrier options by Fourier-cosine series expansions, Numer. Math., 114, 27-62 (2009) · Zbl 1185.91176 · doi:10.1007/s00211-009-0252-4
[6] Yang, Y.; Su, W.; Zhang, Z., Estimating the discounted density of the deficit at ruin by Fourier cosine series expansion, Stat. Probab. Lett., 146, 147-155 (2019) · Zbl 1450.62133 · doi:10.1016/j.spl.2018.11.015
[7] Chan, T. L.R., Hedging and pricing early-exercise options with complex Fourier series expansion, N. Am. J. Econ. Finance, 2019 (2019)
[8] Ibrahim, S. N.I.; Ng, T. W., Fourier-based approach for power options valuation, Malaysian J. Math. Sci., 13, 31-40 (2019) · Zbl 1427.91277
[9] Lin, S.; He, X. J., A regime switching fractional Black-Scholes model and European option pricing, Commun. Nonlinear Sci. Numer. Simul., 85 (2020) · Zbl 1448.91299 · doi:10.1016/j.cnsns.2020.105222
[10] Ma, J.; Wang, H., Convergence rates of moving mesh methods for moving boundary partial integro-differential equations from regime-switching jump-diffusion Asian option pricing, J. Comput. Appl. Math., 370 (2020) · Zbl 1447.65029 · doi:10.1016/j.cam.2019.112598
[11] Drapeau, S.; Luo, P.; Xiong, D., Characterization of fully coupled FBSDE in terms of portfolio optimization, Electron. J. Probab., 25, 1-26 (2020) · Zbl 1444.60068
[12] Xie, B.; Yu, Z., An exploration of \(L_p\)-theory for forward-backward stochastic differential equations with random coefficients on small durations, J. Math. Anal. Appl., 483, 2 (2020) · Zbl 1471.60092 · doi:10.1016/j.jmaa.2019.123642
[13] Ruijter, M. J.; Oosterlee, C. W., Two-dimensional Fourier cosine series expansion method for pricing financial options, SIAM J. Sci. Comput., 34, 642-671 (2012) · Zbl 1258.91222 · doi:10.1137/120862053
[14] Meng, Q. J.; Ding, D., An efficient pricing method for rainbow options based on two-dimensional modified sine-sine series expansions, Int. J. Comput. Math., 90, 1096-1113 (2013) · Zbl 1277.91195 · doi:10.1080/00207160.2012.749349
[15] Ding, D.; Li, X.; Liu, Y., A regression-based numerical scheme for backward stochastic differential equations, Comput. Stat., 32, 1357-1373 (2017) · Zbl 1417.65021 · doi:10.1007/s00180-017-0763-x
[16] Zhao, W.; Chen, L.; Peng, S. G., A new kind of accurate numerical method for backward stochastic differential equations, SIAM J. Sci. Comput., 28, 1563-1581 (2006) · Zbl 1121.60072 · doi:10.1137/05063341X
[17] Bender, C.; Zhang, J., Time discretization and Markovian iteration for coupled FBSDEs, Ann. Appl. Probab., 18, 143-177 (2008) · Zbl 1142.65005 · doi:10.1214/07-AAP448
[18] Bouchard, B.; Ekeland, I.; Touzi, N., On the Malliavin approach to Monte Carlo approximation of conditional expectations, Finance Stoch., 8, 45-71 (2004) · Zbl 1051.60061 · doi:10.1007/s00780-003-0109-0
[19] Bouchard, B.; Touzi, N., Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations, Stoch. Process. Appl., 111, 175-206 (2004) · Zbl 1071.60059 · doi:10.1016/j.spa.2004.01.001
[20] Crimaldi, I.; Pratelli, L., Convergence results for conditional expectations, Bernoulli, 11, 737-745 (2005) · Zbl 1114.60024 · doi:10.3150/bj/1126126767
[21] Li, Y.; Yang, J.; Zhao, W., Convergence error estimates of the Crank-Nicolson scheme for solving decoupled FBSDEs, Sci. China Math., 60, 923-948 (2017) · Zbl 1372.65018 · doi:10.1007/s11425-016-0178-8
[22] Sun, Y.; Zhao, W., New second-order schemes for forward backward stochastic differential equations, East Asian J. Appl. Math., 8, 399-421 (2018) · Zbl 1478.65009 · doi:10.4208/eajam.100118.070318
[23] Boyd, J. P., Chebyshev & Fourier Spectral Methods (2001), Mineola: Dover, Mineola · Zbl 0994.65128
[24] Gobet, E.; Lemor, J. P.; Warin, X., A regression-based Monte Carlo method to solve backward stochastic differential equations, Ann. Appl. Probab., 15, 2172-2202 (2005) · Zbl 1083.60047 · doi:10.1214/105051605000000412
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