Found 175 Documents (Results 1–100)
Recent developments in machine learning methods for stochastic control and games. (English) Zbl 07923331
Novel multi-step predictor-corrector schemes for backward stochastic differential equations. (English) Zbl 07912563
Linear-quadratic Pareto cooperative game for mean-field backward stochastic system. (English) Zbl 07903341
A deep learning method for solving multi-dimensional coupled forward-backward doubly SDEs. (English) Zbl 07894803
Solvability of one kind of forward-backward stochastic difference equations. (English) Zbl 07887794
MSC:
62-XX
Richardson extrapolation of the Crank-Nicolson scheme for backward stochastic differential equations. (English) Zbl 07874382
A mild approach to spatial discretization for backward stochastic differential equations in infinite dimensions. (English) Zbl 07834379
Deep learning algorithms for solving high-dimensional nonlinear backward stochastic differential equations. (English) Zbl 1532.60153
Convergence of the backward deep BSDE method with applications to optimal stopping problems. (English) Zbl 1527.60031
Splitting scheme for backward doubly stochastic differential equations. (English) Zbl 1528.60065
Reviewer: Maria Gordina (Storrs)
Approximation and error analysis of forward-backward SDEs driven by general Lévy processes using shot noise series representations. (English) Zbl 1517.60065
Forward-backward stochastic differential equations: initiation, development and beyond. (English) Zbl 1515.60227
A sample-wise data driven control solver for the stochastic optimal control problem with unknown model parameters. (English) Zbl 1520.93605
Temporal semi-discretizations of a backward semilinear stochastic evolution equation. (English) Zbl 1515.65028
Stability of backward stochastic differential equations: the general Lipschitz case. (English) Zbl 1520.60050
Reviewer: Alexandra Rodkina (College Station)
Strong stability preserving multistep schemes for forward backward stochastic differential equations. (English) Zbl 1516.65003
A stochastic maximum principle approach for reinforcement learning with parameterized environment. (English) Zbl 07696994
Deep xVA solver: a neural network-based counterparty credit risk management framework. (English) Zbl 1516.91065
Numerical methods for backward stochastic differential equations: a survey. (English) Zbl 1515.65023
Overcoming the curse of dimensionality in the numerical approximation of backward stochastic differential equations. (English) Zbl 1515.65025
Reviewer: Kevin Burrage (Brisbane)
Convergence of a spatial semidiscretization for a backward semilinear stochastic parabolic equation. (English) Zbl 1517.49017
Reviewer: Latifa Debbi (M’Sila)
Stochastic optimal and time-optimal control studies for additional food provided prey-predator systems involving Holling type III functional response. (English) Zbl 1508.92225
Solving BSDEs based on novel multi-step schemes and multilevel Monte Carlo. (English) Zbl 1499.60249
A multi-step algorithm for BSDEs based on a predictor-corrector scheme and least-squares Monte Carlo. (English) Zbl 1505.65002
Deep learning schemes for parabolic nonlocal integro-differential equations. (English) Zbl 1515.60249
Solvability of forward-backward stochastic difference equations with finite states. (English) Zbl 1505.39017
Convolutional neural network based simulation and analysis for backward stochastic partial differential equations. (English) Zbl 1524.60120
Quantitative stability and numerical analysis of Markovian quadratic BSDEs with reflection. (English) Zbl 1487.65012
A Fourier transform method for solving backward stochastic differential equations. (English) Zbl 1487.65008
An explicit multistep scheme for mean-field forward-backward stochastic differential equations. (English) Zbl 1499.65021
Multistep schemes for solving backward stochastic differential equations on GPU. (English) Zbl 1485.91251
Approximation error analysis of some deep backward schemes for nonlinear PDEs. (English) Zbl 1490.65231
Algorithms for solving high dimensional PDEs: from nonlinear Monte Carlo to machine learning. (English) Zbl 1490.60202
Multilevel Picard iterations for solving smooth semilinear parabolic heat equations. (English) Zbl 1476.65273
Solving high-dimensional Hamilton-Jacobi-Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path space. (English) Zbl 1480.35101
Approximation of BSDEs with super-linearly growing generators by Euler’s polygonal line method: a simple proof of the existence. (English) Zbl 1475.60107
Decoupling on the Wiener space, related Besov spaces, and applications to BSDEs. (English) Zbl 1494.60002
Memoirs of the American Mathematical Society 1335. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-4935-3/pbk; 978-1-4704-6751-7/ebook). iv, 112 p. (2021).
Reviewer: Isamu Dôku (Saitama)
Branching diffusion representation for nonlinear Cauchy problems and Monte Carlo approximation. (English) Zbl 1476.35090
Path dependent optimal transport and model calibration on exotic derivatives. (English) Zbl 1479.60144
Duality and approximation of stochastic optimal control problems under expectation constraints. (English) Zbl 1471.93283
Strong rates of convergence for a space-time discretization of the backward stochastic heat equation, and of a linear-quadratic control problem for the stochastic heat equation. (English) Zbl 1467.60050
Data informed solution estimation for forward-backward stochastic differential equations. (English) Zbl 1475.60100
An efficient numerical method for forward-backward stochastic differential equations driven by \(G\)-Brownian motion. (English) Zbl 1484.65012
High-order combined multi-step scheme for solving forward backward stochastic differential equations. (English) Zbl 07353297
Discretization of a distributed optimal control problem with a stochastic parabolic equation driven by multiplicative noise. (English) Zbl 1479.60132
Reviewer: Martin Gugat (Erlangen)
Some analytic approximations for backward stochastic differential equations. (English) Zbl 1499.60248
Mean square rate of convergence for random walk approximation of forward-backward SDEs. (English) Zbl 1473.60089
A stochastic maximum principle for partially observed stochastic control systems with delay. (English) Zbl 1454.93297
Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks. (English) Zbl 1469.60220
A unified probabilistic discretization scheme for FBSDEs: stability, consistency, and convergence analysis. (English) Zbl 1454.60106
A new numerical method for 1-D backward stochastic differential equations without using conditional expectations. (English) Zbl 1461.60042
Reviewer: Melvin D. Lax (Long Beach)
Branching diffusion representation of semi-linear elliptic PDEs and estimation using Monte Carlo method. (English) Zbl 1440.35125
Spatial convergence for semi-linear backward stochastic differential equations in Hilbert space: a mild approach. (English) Zbl 1449.60105
Weighted bounded mean oscillation applied to backward stochastic differential equations. (English) Zbl 1444.60053
An implicit numerical scheme for a class of backward doubly stochastic differential equations. (English) Zbl 1467.60040
Reviewer: Nikolaos Halidias (Athína)
\( L^2\)-regularity result for solutions of backward doubly stochastic differential equations. (English) Zbl 1505.60060
\(L^2\)-regularity of solutions to linear backward stochastic heat equations, and a numerical application. (English) Zbl 1441.60050
A multi-step scheme based on cubic spline for solving backward stochastic differential equations. (English) Zbl 1433.60041
Random walk approximation of BSDEs with Hölder continuous terminal condition. (English) Zbl 1433.60033
On the uniqueness of solutions to quadratic BSDEs with non-convex generators. (English) Zbl 1498.60201
Cohen, Samuel N. (ed.) et al., Frontiers in stochastic analysis – BSDEs, SPDEs and their applications. International workshop on BSDEs, SPDEs and their applications, Edinburgh, UK, July 3–7, 2017. Selected, revised and extended contributions. Cham: Springer. Springer Proc. Math. Stat. 289, 89-107 (2019).
MSC:
60H10
Backward stochastic Volterra integral equations – representation of adapted solutions. (English) Zbl 1427.60140
Higher-order discretization methods of forward-backward SDEs using KLNV-scheme and their applications to XVA pricing. (English) Zbl 1426.91273
Asymptotic expansion as prior knowledge in deep learning method for high dimensional BSDEs. (English) Zbl 1422.91694
Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations. (English) Zbl 1442.91116
A numerical method for forward-backward stochastic equations with delay and anticipated term. (English) Zbl 1433.60044
On multilevel Picard numerical approximations for high-dimensional nonlinear parabolic partial differential equations and high-dimensional nonlinear backward stochastic differential equations. (English) Zbl 1418.65149
Numerical approximation of general Lipschitz BSDEs with branching processes. (English. French summary) Zbl 1416.60070
Numerical approximations of McKean anticipative backward stochastic differential equations arising in initial margin requirements. (English) Zbl 1455.65013
Solving backward stochastic differential equations with quadratic-growth drivers by connecting the short-term expansions. (English) Zbl 1426.60072
MSC:
60H10
A Monte Carlo method for backward stochastic differential equations with Hermite martingales. (English) Zbl 07061108
A backward doubly stochastic differential equation approach for nonlinear filtering problems. (English) Zbl 1488.65008
Pathwise dynamic programming. (English) Zbl 1446.90159
Reviewer: Shyam Sundar Chandramouli (New York)
A kind of LQ non-zero sum differential game of backward stochastic differential equation with asymmetric information. (English) Zbl 1420.91022
General linear forward and backward stochastic difference equations with applications. (English) Zbl 1406.93387
Convergence and qualitative properties of modified explicit schemes for BSDEs with polynomial growth. (English) Zbl 06974758
Improved error bounds for quantization based numerical schemes for BSDE and nonlinear filtering. (English) Zbl 1390.60152
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