On Multilevel Picard Numerical Approximations for High-Dimensional Nonlinear Parabolic Partial Differential Equations and High-Dimensional Nonlinear Backward Stochastic Differential Equations
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E Weinan | Arnulf Jentzen | Thomas Kruse | Martin Hutzenthaler | W. E | E. Weinan | M. Hutzenthaler | Arnulf Jentzen | T. Kruse | Martin Hutzenthaler
[1] D. Talay,et al. Stochastic simulation and Monte-Carlo methods , 2013 .
[2] Marc L. Ross. Counterparty Risk and Funding: The Four Wings of the TVA , 2013 .
[3] P. Protter,et al. Numberical Method for Backward Stochastic Differential Equations , 2002 .
[4] Numérisation de documents anciens mathématiques,et al. Mathematical modelling and numerical analysis : Modélisation mathématique et analyse numérique. , 1985 .
[5] Christoph Burgard,et al. Partial Differential Equation Representations of Derivatives with Bilateral Counterparty Risk and Funding Costs , 2010 .
[6] Jin Ma,et al. Representation theorems for backward stochastic differential equations , 2002 .
[7] Carl Graham,et al. Stochastic Simulation and Monte Carlo Methods: Mathematical Foundations of Stochastic Simulation , 2013 .
[8] Yaacov Z. Bergman. Option Pricing with Differential Interest Rates , 1995 .
[9] Stylianos Perrakis,et al. Option pricing and replication with transaction costs and dividends , 2000 .
[10] Jie Xiong,et al. A branching particle system approximation for a class of FBSDEs , 2016 .
[11] Emmanuel Gobet,et al. Generalized fractional smoothness and Lp-variation of BSDEs with non-Lipschitz terminal condition , 2011, 1103.0371.
[12] Shige Peng,et al. Probabilistic interpretation for systems of quasilinear parabolic partial differential equations , 1991 .
[13] Plamen Turkedjiev,et al. Two algorithms for the discrete time approximation of Markovian backward stochastic differential equations under local conditions , 2013, 1309.4378.
[14] Terry Lyons,et al. Cubature on Wiener space , 2004, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.
[15] B. Delyon,et al. DONSKER-TYPE THEOREM FOR BSDES , 2001 .
[16] Pratima Hebbar. Branching diffusion processes in periodic media , 2019 .
[17] H. Leland.. Option Pricing and Replication with Transactions Costs , 1985 .
[18] Anna Lisa Amadori,et al. Nonlinear integro-differential evolution problems arising in option pricing: a viscosity solutions approach , 2003, Differential and Integral Equations.
[19] Nadia Oudjane,et al. Branching diffusion representation of semilinear PDEs and Monte Carlo approximation , 2016, Annales de l'Institut Henri Poincaré, Probabilités et Statistiques.
[20] Céline Labart,et al. Solving BSDE with Adaptive Control Variate , 2010, SIAM J. Numer. Anal..
[21] Nizar Touzi,et al. A Probabilistic Numerical Method for Fully Nonlinear Parabolic PDEs , 2009, 0905.1863.
[22] C. Litterer,et al. High order recombination and an application to cubature on Wiener space , 2010 .
[23] Dan Crisan,et al. Probabilistic methods for semilinear partial differential equations. Applications to finance , 2010 .
[24] W. E,et al. Multilevel Picard iterations for solving smooth semilinear parabolic heat equations , 2016, Partial Differential Equations and Applications.
[25] Giuseppe Da Prato,et al. Differentiability of the Feynman-Kac semigroup and a control application , 1997 .
[26] Jia Zhuo,et al. A monotone scheme for high-dimensional fully nonlinear PDEs , 2012, 1212.0466.
[27] E. Tadmor. A review of numerical methods for nonlinear partial differential equations , 2012 .
[28] Christel Geiss,et al. Simulation of BSDEs with jumps by Wiener Chaos expansion , 2015, 1502.05649.
[29] Michael B. Giles,et al. Multilevel Monte Carlo Path Simulation , 2008, Oper. Res..
[30] Anton Wakolbinger,et al. Length of Galton-Watson trees and blow-up of semilinear systems , 1998 .
[31] Stefan Heinrich,et al. Multilevel Monte Carlo Methods , 2001, LSSC.
[32] M. Hutzenthaler,et al. On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with non-globally monotone coefficients , 2014, 1401.0295.
[33] Miguel A. Herrero,et al. Boundedness and blow up for a semilinear reaction-diffusion system , 1991 .
[34] Robert Denk,et al. A forward scheme for backward SDEs , 2007 .
[35] S. Menozzi,et al. A Forward-Backward Stochastic Algorithm For Quasi-Linear PDEs , 2006, math/0603250.
[36] E. Gobet,et al. A regression-based Monte Carlo method to solve backward stochastic differential equations , 2005, math/0508491.
[37] Dan Crisan,et al. Minimal Entropy Approximations and Optimal Algorithms , 2002, Monte Carlo Methods Appl..
[38] Peter A. Forsyth,et al. Hedging with a correlated asset: Solution of a nonlinear pricing PDE , 2007 .
[39] E. Bayraktar,et al. Pricing options in incomplete equity markets via the instantaneous Sharpe ratio , 2007, math/0701650.
[40] Cornelis W. Oosterlee,et al. A Fourier-Cosine Method for an Efficient Computation of Solutions to BSDEs , 2013, SIAM J. Sci. Comput..
[41] G. Pagès,et al. A quantization algorithm for solving multidimensional discrete-time optimal stopping problems , 2003 .
[42] V. Thomée. Galerkin Finite Element Methods for Parabolic Problems (Springer Series in Computational Mathematics) , 2010 .
[43] Hai-ping Shi. Backward stochastic differential equations in finance , 2010 .
[44] Peter E. Kloeden,et al. Divergence of the multilevel Monte Carlo Euler method for nonlinear stochastic differential equations , 2011, 1105.0226.
[45] M. Nagasawa,et al. PROBABILISTIC TREATMENT OF THE BLOWING UP OF SOLUTIONS FOR A NONLINEAR INTEGRAL EQUATION , 1969 .
[46] Adam Krzyzak,et al. A Distribution-Free Theory of Nonparametric Regression , 2002, Springer series in statistics.
[47] Pierre Henry-Labordere,et al. Counterparty Risk Valuation: A Marked Branching Diffusion Approach , 2012, 1203.2369.
[48] Erhan Bayraktar,et al. Valuation of Mortality Risk via the Instantaneous Sharpe Ratio: Applications to Life Annuities , 2008, 0802.3250.
[49] P. Kloeden,et al. Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients , 2010, 1010.3756.
[50] Emmanuel Gobet,et al. L2-time regularity of BSDEs with irregular terminal functions , 2010 .
[51] G. Maruyama. Continuous Markov processes and stochastic equations , 1955 .
[52] Stefan Heinrich,et al. Monte Carlo Complexity of Global Solution of Integral Equations , 1998, J. Complex..
[53] Jianfeng Zhang. A numerical scheme for BSDEs , 2004 .
[54] Christel Geiss,et al. On approximation of a class of stochastic integrals and interpolation , 2004 .
[55] G. Pagès,et al. Error analysis of the optimal quantization algorithm for obstacle problems , 2003 .
[56] Emmanuel Gobet,et al. Approximation of backward stochastic differential equations using Malliavin weights and least-squares regression , 2016, 1601.01186.
[57] Dan Crisan,et al. Solving Backward Stochastic Differential Equations Using the Cubature Method: Application to Nonlinear Pricing , 2010, SIAM J. Financial Math..
[58] B. Bouchard,et al. Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations , 2004 .
[59] M. Giles. Improved Multilevel Monte Carlo Convergence using the Milstein Scheme , 2008 .
[60] M. Röckner,et al. A Concise Course on Stochastic Partial Differential Equations , 2007 .
[61] Jean-Paul Laurent,et al. An overview of the valuation of collateralized derivative contracts , 2014 .
[62] Steffen Dereich,et al. Infinite-Dimensional Quadrature and Approximation of Distributions , 2009, Found. Comput. Math..
[63] K. Elworthy,et al. Formulae for the Derivatives of Heat Semigroups , 1994, 1911.10971.
[64] C. Schwab,et al. NUMERICAL SOLUTION OF PARABOLIC EQUATIONS IN HIGH DIMENSIONS , 2004 .
[65] Stefan Heinrich,et al. Monte Carlo Complexity of Parametric Integration , 1999, J. Complex..
[66] Emmanuel Gobet,et al. Linear regression MDP scheme for discrete backward stochastic differential equations under general conditions , 2015, Math. Comput..
[67] Stefan Heinrich,et al. The randomized information complexity of elliptic PDE , 2006, J. Complex..
[68] H. Soner,et al. Second‐order backward stochastic differential equations and fully nonlinear parabolic PDEs , 2005, math/0509295.
[69] S. Peng,et al. Backward stochastic differential equations and quasilinear parabolic partial differential equations , 1992 .
[70] S. Peng,et al. Adapted solution of a backward stochastic differential equation , 1990 .
[71] P. Forsyth,et al. Implicit solution of uncertain volatility/transaction cost option pricing models with discretely observed barriers , 2001 .
[72] P. Kloeden,et al. Numerical Solution of Stochastic Differential Equations , 1992 .
[73] Xiaolu Tan,et al. A Numerical Algorithm for a Class of BSDE Via Branching Process , 2013 .
[74] M. Avellaneda,et al. Pricing and hedging derivative securities in markets with uncertain volatilities , 1995 .
[75] Pierre Henry-Labordere,et al. Uncertain Volatility Model: A Monte-Carlo Approach , 2010 .
[76] Arnaud Lionnet,et al. Time discretization of FBSDE with polynomial growth drivers and reaction-diffusion PDEs , 2013, 1309.2865.
[77] N. Touzi,et al. On the Monte Carlo simulation of BSDEs: An improvement on the Malliavin weights , 2010 .
[78] P. Briand,et al. Simulation of BSDEs by Wiener Chaos Expansion , 2012, 1204.4137.
[79] Emmanuel Gobet,et al. Numerical simulation of BSDEs using empirical regression methods: theory and practice , 2005 .
[80] Cornelis W. Oosterlee,et al. Generalized beta regression models for random loss given default , 2008 .
[81] E. Gobet,et al. Rate of convergence of an empirical regression method for solving generalized backward stochastic differential equations , 2006 .
[82] Dan Crisan,et al. RUNGE-KUTTA SCHEMES FOR BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS , 2014 .
[83] Jean-François Chassagneux,et al. Linear Multistep Schemes for BSDEs , 2014, SIAM J. Numer. Anal..
[84] D. Crisan,et al. Second order discretization of backward SDEs and simulation with the cubature method , 2014 .
[85] P. Kloeden,et al. Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients , 2009, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.
[86] D. Duffie,et al. Recursive valuation of defaultable securities and the timing of resolution of uncertainty , 1996 .
[87] Christian Bender,et al. A PRIMAL–DUAL ALGORITHM FOR BSDES , 2013, 1310.3694.
[88] H. Fujita. On the blowing up of solutions fo the Cauchy problem for u_t=Δu+u^ , 1966 .
[89] E Weinan,et al. On full history recursive multilevel Picard approximations and numerical approximations for high-dimensional nonlinear parabolic partial differential equations and high-dimensional nonlinear backward stochastic differential equations , 2016 .
[90] Cornelis W. Oosterlee,et al. Numerical Fourier Method and Second-Order Taylor Scheme for Backward SDEs in Finance , 2014 .
[91] Francesco Russo,et al. Forward Feynman-Kac type representation for semilinear non-conservative partial differential equations , 2016, Stochastics.