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Parabolic partial differential equations (PDEs) and backward stochastic differential equations (BSDEs) are key ingredients in a number of models in physics and financial engineering.
Continuous Markov processes and stochastic equations
1955
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Quadrature and interpolation formulas for tensor products of certain classes of functions
1963
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Branching diffusion processes
1964
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Probabilistic treatment of the blowing up of solutions for a nonlinear integral equation
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Option pricing and replication with transaction costs
1985
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Adapted solution of a backward stochastic differential equation
1990
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Boundedness and blow up for a semilinear reaction-diffusion system
1991
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Probabilistic interpretation for systems of quasilinear parabolic partial differential equations
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Numerical solution of stochastic differential equations
1992
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Backward stochastic differential equations and quasilinear parabolic partial differential equations
1992
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Formulae for the derivatives of heat semigroups
1994
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Pricing and hedging derivative securities in markets with uncertain volatilities
1995
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Option pricing with differential interest rates
1995
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Recursive valuation of defaultable securities and the timing of resolution of uncertainty
1996
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Differentiability of the Feynman-Kac semigroup and a control application
1997
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Backward stochastic differential equations in finance
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Galerkin finite element methods for parabolic problems
1997
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Monte Carlo complexity of global solution of integral equations
1998
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Monte Carlo complexity of parametric integration
1998
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Length of Galton-Watson trees and blow-up of semilinear systems
1998
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Donsker-type theorem for BSDEs
2001
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Implicit solution of uncertain volatility/transaction cost option pricing models with discretely observed barriers
2001
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Multilevel Monte Carlo Methods
2001
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Minimal entropy approximations and optimal algorithms for the filtering problem
2002
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Numberical method for backward stochastic differential equations
2002
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Nonlinear integro-differential evolution problems arising in option pricing: a viscosity solutions approach
2003
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Error analysis of the optimal quantization algorithm for obstacle problems
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A quantization algorithm for solving multi-dimensional discrete-time optimal stopping problems
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Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations
2004
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On approximation of a class of stochastic integrals and interpolation
2004
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Cubature on Wiener space
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Numerical solution of parabolic equations in high dimensions
2004
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A numerical scheme for BSDEs
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A regression-based Monte Carlo method to solve backward stochastic differential equations
2005
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A forward-backward stochastic algorithm for quasi-linear PDEs
Counterparty risk valuation: a marked branching diffusion approach
2012
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Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients
2012
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High order recombination and an application to cubature on Wiener space
2012
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A review of numerical methods for nonlinear partial differential equations
2012
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Counterparty risk and funding: the four wings of the TVA
2013
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Stochastic simulation and Monte Carlo methods
2013
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2006
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The randomized information complexity of elliptic PDE
2006
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Rate of convergence of an empirical regression method for solving generalized backward stochastic differential equations
2006
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A forward scheme for backward SDEs
2007
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Second-order backward stochastic differential equations and fully nonlinear parabolic PDEs
2007
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A concise course on stochastic partial differential equations
2007
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Simulation of BSDEs by Wiener chaos expansion
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Linear multistep schemes for BSDEs
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Runge–Kutta schemes for backward stochastic differential equations
2014
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Second order discretization of backward SDEs and simulation with the cubature method
2014
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A numerical algorithm for a class of BSDEs via the branching process
2014
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2014
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An overview of the valuation of collateralized derivative contracts
2014
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A primal–-dual algorithm for BSDEs
2015
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A monotone scheme for high-dimensional fully nonlinear PDEs
2015
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Time discretization of FBSDE with polynomial growth drivers and reaction–diffusion PDEs
2015
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A Fourier cosine method for an efficient computation of solutions to BSDEs
2015
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Two algorithms for the discrete time approximation of Markovian backward stochastic differential equations under local conditions
2015
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A branching particle system approximation for a class of FBSDEs
2016
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Simulation of BSDEs with jumps by Wiener Chaos expansion
2016
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Approximation of backward stochastic differential equations using Malliavin weights and least-squares regression
2016
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Linear regression MDP scheme for discrete backward stochastic differential equations under general conditions
2016
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Branching diffusion representation of semilinear PDEs and Monte Carlo approximation
2016
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2016
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Numerical Fourier method and second-order Taylor scheme for backward SDEs in finance
2016
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Linear scaling algorithms for solving high-dimensional nonlinear parabolic differential equations
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