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We introduce a new family of numerical algorithms for approximating solutions of general high-dimensional semilinear parabolic partial differential equations at single space-time points.
Continuous Markov processes and stochastic equations
1955
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A remark on stirling’s formula
1955
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Dynamic programming
1957
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Branching diffusion processes
1964
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Adapted solution of a backward stochastic differential equation
1990
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Stochastic differential equations in infinite dimensions: solutions via dirichlet forms
1991
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Brownian motion and stochastic calculus
1991
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Probabilistic interpretation for systems of quasilinear parabolic partial differential equations
1991
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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
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Option pricing with differential interest rates
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Recursive valuation of defaultable securities and the timing of resolution of uncertainty
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Existence of strong solutions for Itô’s stochastic equations via approximations
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Differentiability of the Feynman-Kac semigroup and a control application
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Monte Carlo complexity of global solution of integral equations
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Stochastic controls
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Difference Equations and Inequalities: Theory, Methods, and Applications
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Multilevel Monte Carlo Methods
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A quantization algorithm for solving multi-dimensional discrete-time optimal stopping problems
2003
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Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations
Multilevel Monte Carlo path simulation
2008
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Infinite-dimensional quadrature and approximation of distributions
2009
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Solving BSDE with adaptive control variate
2010
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Partial differential equation representations of derivatives with bilateral counterparty risk and funding costs
2011
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Solving backward stochastic differential equations using the cubature method: Application to nonlinear pricing
2012
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Counterparty risk valuation: a marked branching diffusion approach
2012
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2004
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A regression-based Monte Carlo method to solve backward stochastic differential equations
2005
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Statistical Romberg extrapolation: a new variance reduction method and applications to option pricing
2005
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A forward scheme for backward SDEs
2007
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Methods of numerical integration
2007
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Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients
2012
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Stochastic simulation and Monte Carlo methods
2013
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Simulation of BSDEs by Wiener chaos expansion
2014
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Linear multistep schemes for BSDEs
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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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