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Beliaev, Dmitry (ed.) et al., International congress of mathematicians 2022, ICM 2022, Helsinki, Finland, virtual, July 6–14, 2022. Volume 2. Plenary lectures. Berlin: European Mathematical Society (EMS). 914-954 (2023).

MSC: 68T05 35K55 41A30 65D40 68T07 90C90 93E03

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Xu, Ruimin; Zhou, Ying

Risk-sensitive stochastic maximum principle for forward-backward systems involving Impulse controls. (English) Zbl 1533.93854

Int. J. Robust Nonlinear Control 33, No. 18, 10990-10999 (2023).

MSC: 93E20 49N10 93C27

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Fang, Shuixin; Zhao, Weidong

ODE-based multistep schemes for backward stochastic differential equations. (English) Zbl 07814777

Numer. Math., Theory Methods Appl. 16, No. 4, 1053-1086 (2023).

MSC: 65C30 60H35 65C20

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Zhou, Jianjun

Viscosity solutions to second order path-dependent Hamilton-Jacobi-Bellman equations and applications. (English) Zbl 07791542

Ann. Appl. Probab. 33, No. 6B, 5564-5612 (2023).

MSC: 93E20 60H30 49L12 49L20 49L25

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Hun, O.; Kim, Mun-Chol; Kim, Kon-Gun

Dynamic programming approach to reflected backward stochastic differential equations. (English) Zbl 07790277

Electron. J. Probab. 28, Paper No. 114, 20 p. (2023).

MSC: 60H10 60H30

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Essaky, E. H.; Hassani, M.; Rhazlane, C. E.

Backward stochastic evolution inclusions in UMD Banach spaces. (English) Zbl 1528.60058

Infin. Dimens. Anal. Quantum Probab. Relat. Top. 26, No. 4, Article ID 2350013, 40 p. (2023).

MSC: 60H10 60H15 47D06

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Baroun, Mahmoud; Boulite, Said; Elgrou, Abdellatif; Maniar, Lahcen

Null controllability for stochastic parabolic equations with dynamic boundary conditions. (English) Zbl 1537.93081

J. Dyn. Control Syst. 29, No. 4, 1727-1756 (2023).

Reviewer: Juan Ramón Torregrosa Sánchez (València)

MSC: 93B05 93B07 93E20 60H15

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Duan, Junxia; Peng, Jun

The probabilistic solution of a system of semilinear elliptic PDEs under the third boundary conditions. (English) Zbl 1531.35144

Potential Anal. 59, No. 4, 1571-1597 (2023).

MSC: 35J57 35J61 31C25 60H15 60J60

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Peng, Shige; Song, Yongsheng; Wang, Falei

Survey on path-dependent PDEs. (English) Zbl 1527.60041

Chin. Ann. Math., Ser. B 44, No. 6, 837-856 (2023).

MSC: 60H10 35F20 60H30 35K10

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Wang, Tianxiao; Yong, Jiongmin

Spike variations for stochastic Volterra integral equations. (English) Zbl 1530.45002

SIAM J. Control Optim. 61, No. 6, 3608-3634 (2023).

MSC: 45D05 45R05 60H20 93C30

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Baadi, Brahim; Marzougue, Mohamed

Existence and uniqueness for reflected BSDE with multivariate point process and right upper semicontinuous obstacle. (English) Zbl 1525.60069

Random Oper. Stoch. Equ. 31, No. 4, 351-370 (2023).

MSC: 60H10 60G40 60G55

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Yang, Minglei; Zhang, Guannan; Del-Castillo-Negrete, Diego; Cao, Yanzhao

A probabilistic scheme for semilinear nonlocal diffusion equations with volume constraints. (English) Zbl 07770183

SIAM J. Numer. Anal. 61, No. 6, 2718-2743 (2023).

MSC: 68Q25 65M75 60J60 65C30

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Xu, Jie; Lian, Qiqi

A strong convergence rate of the averaging principle for two-time-scale forward-backward stochastic differential equations. (English) Zbl 1535.60109

J. Theor. Probab. 36, No. 4, 2590-2610 (2023).

MSC: 60H10 70K65 70K70

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Owo, Jean-Marc; Aman, Auguste

Generalized backward doubly stochastic differential equations driven by Lévy processes with discontinuous and linear growth coefficients. (English) Zbl 07768807

J. Theor. Probab. 36, No. 4, 2311-2338 (2023).

MSC: 60G51 60H10 91G20 60H30

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Li, Xinying; Lai, Yuru; Fan, Shengjun

BSDEs with stochastic Lipschitz condition: a general result. (English) Zbl 1535.60102

Probab. Uncertain. Quant. Risk 8, No. 2, 267-280 (2023).

MSC: 60H10

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Gu, Zihao; Lin, Yiqing; Xu, Kun

Quadratic BSDEs with mean reflection driven by \(G\)-Brownian motion. (English) Zbl 1535.60098

Stoch. Dyn. 23, No. 5, Article ID 2350044, 41 p. (2023).

MSC: 60H10 60G65

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Shi, Yufeng; Yang, Zhi

Existence result for the BSDE with superquadratic growth. (English) Zbl 07767162

Commun. Stat., Theory Methods 52, No. 24, 8902-8908 (2023).

MSC: 62-XX

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Hawkins, Kelsey P.; Pakniyat, Ali; Tsiotras, Panagiotis

Value function estimators for Feynman-Kac forward-backward SDEs in stochastic optimal control. (English) Zbl 1530.93544

Automatica 158, Article ID 111281, 10 p. (2023).

MSC: 93E20 93E10 60H30

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Shi, Xuejun; Jiang, Long

Representation theorem and viability property for multidimensional BSDEs and their applications. (English) Zbl 1523.60102

Probab. Uncertain. Quant. Risk 8, No. 3, 373-390 (2023).

MSC: 60H10

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Shi, Yufeng; Yang, Zhi

On the uniqueness result for the BSDE with deterministic coefficient. (English) Zbl 1523.60103

Probab. Uncertain. Quant. Risk 8, No. 3, 309-320 (2023).

MSC: 60H10

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Klimsiak, Tomasz; Rzymowski, Maurycy

Nonlinear BSDEs with two optional Doob’s class barriers satisfying weak Mokobodzki’s condition and extended Dynkin games. (English) Zbl 1523.60100

Appl. Math. Optim. 88, No. 3, Paper No. 80, 33 p. (2023).

MSC: 60H10 60G40

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Aidara, Sadibou; Ndiaye, Assane; Sow, Ahmadou Bamba

Generalized BDSDEs driven by fractional Brownian motion. (English) Zbl 1524.60116

Nonauton. Dyn. Syst. 10, Article ID 20220167, 11 p. (2023).

MSC: 60H10 60H07 60G22

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Boufoussi, Brahim; Mouchtabih, Soufiane

McKean-Vlasov BSDEs with locally monotone coefficient. (English) Zbl 1540.60105

Acta Math. Sin., Engl. Ser. 39, No. 7, 1414-1424 (2023).

MSC: 60H10

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Aidara, Sadibou; Sane, Ibrahima

Delay BSDEs driven by fractional Brownian motion. (English) Zbl 1525.60067

Random Oper. Stoch. Equ. 31, No. 3, 273-284 (2023).

MSC: 60H10 60H07 60G22 60G44

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Elmansouri, Badr; El Otmani, Mohamed

Generalized backward stochastic differential equations with jumps in a general filtration. (English) Zbl 1539.60069

Random Oper. Stoch. Equ. 31, No. 3, 205-216 (2023).

MSC: 60H10 34F05 60H15 35R60 60H20 60H30 60H05

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Schütte, Christof; Klus, Stefan; Hartmann, Carsten

Overcoming the timescale barrier in molecular dynamics: transfer operators, variational principles and machine learning. (English) Zbl 07736659

Acta Numerica 32, 517-673 (2023).

MSC: 65-XX 37M10 37M25 82C31 82M37 47D07 60J35 60J60

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Di Persio, Luca; Garbelli, Matteo; Zălinescu, Adrian

Feynman-Kac formula for BSDEs with jumps and time delayed generators associated to path-dependent nonlinear Kolmogorov equations. (English) Zbl 1523.35312

NoDEA, Nonlinear Differ. Equ. Appl. 30, No. 6, Paper No. 72, 36 p. (2023).

MSC: 35R60 60H15 60G51 60H30

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An, Lifen; Cohen, Samuel N.; Ji, Shaolin

Reflected backward stochastic difference equations and optimal stopping problems under \(g\)-expectation. (English) Zbl 1533.60084

Electron. J. Probab. 28, Paper No. 99, 24 p. (2023).

MSC: 60H10 60G40 91G80

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Massing, Till

Approximation and error analysis of forward-backward SDEs driven by general Lévy processes using shot noise series representations. (English) Zbl 1517.60065

ESAIM, Probab. Stat. 27, 694-722 (2023).

MSC: 60H10 60H35 65C05

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Aidara, Sadibou; Sagna, Yaya; Faye, Ibrahima

Averaging principle for BSDEs driven by two mutually independent fractional Brownian motions. (English) Zbl 1517.60057

Appl. Anal. 102, No. 8, 2189-2199 (2023).

MSC: 60H10 60H05 60G22

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Castro, Javier

The Kolmogorov infinite dimensional equation in a Hilbert space via deep learning methods. (English) Zbl 07723298

J. Math. Anal. Appl. 527, No. 2, Article ID 127413, 40 p. (2023).

MSC: 68Qxx 68Txx 60H15 60H35 65M75 60H30 35K55

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Oualaid, Abdelkarim; Bahlali, Khaled; Ouknine, Youssef

Reflected backward stochastic differential equations associated to jump Markov processes and application to partial differential equations. (English) Zbl 1532.60171

J. Theor. Probab. 36, No. 3, 1400-1436 (2023).

Reviewer: Nicolas Privault (Singapura)

MSC: 60J76 60H10 60G57 35A23 35D40 49J40

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Djehiche, Boualem; Elie, Romuald; Hamadène, Said

Mean-field reflected backward stochastic differential equations. (English) Zbl 1515.60182

Ann. Appl. Probab. 33, No. 4, 2493-2518 (2023).

MSC: 60H10 60H07 49N90

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Found 1,289 Documents (Results 1–100)

Stochastic recursive optimal control of McKean-Vlasov type: a viscosity solution approach. (English) Zbl 07923494

Recent developments in machine learning methods for stochastic control and games. (English) Zbl 07923331

Optimal relaxed control for a decoupled \(G\)-FBSDE. (English) Zbl 07922474

Semimartingale dynamics for a backward exchange rate process. (English) Zbl 07920275

Capital allocation for cash-subadditive risk measures: from BSDEs to BSVIEs. (English) Zbl 07920274

Partially observed mean-field game and related mean-field forward-backward stochastic differential equation. (English) Zbl 07919101

Efficient drift parameter estimation for ergodic solutions of backward SDEs. (English) Zbl 07916038

BSDEs driven by fractional Brownian motion with time-delayed generators. (English) Zbl 07915834

Novel multi-step predictor-corrector schemes for backward stochastic differential equations. (English) Zbl 07912563

Two-player zero-sum stochastic differential games with regime switching and corresponding Hamilton-Jacobi-Bellman-Isaacs’ equations. (English) Zbl 07908359

Averaging principle for BSDEs driven by fractional Brownian motion with non Lipschitz coefficients. (English) Zbl 07906598

Optimal controls for forward-backward stochastic differential equations: time-inconsistency and time-consistent solutions. (English. French summary) Zbl 07906238

Backward doubly stochastic differential equations and SPDEs with quadratic growth. (English) Zbl 07904808

Optimal stopping: Bermudan strategies meet non-linear evaluations. (English) Zbl 07904064

Explicit solution to delayed forward and backward stochastic differential equations. (English) Zbl 07903843

Linear-quadratic Pareto cooperative game for mean-field backward stochastic system. (English) Zbl 07903341

General mean-field BSDEs with diagonally quadratic generator in multi-dimension. (English) Zbl 07901497

Fully coupled forward-backward stochastic differential equations driven by sub-diffusions. (English) Zbl 07901389

Multi-dimensional reflected backward stochastic differential equations driven by \(G\)-Brownian motion with diagonal generators. (English) Zbl 07900859

Mixed Nash games and social optima for linear-quadratic forward-backward mean-field systems. (English) Zbl 07897765

A deep learning method for solving multi-dimensional coupled forward-backward doubly SDEs. (English) Zbl 07894803

Non-zero-sum differential games of delayed backward doubly stochastic systems and their application. (English) Zbl 07892508

Mean reflected BSDE driven by a marked point process and application in insurance risk management. (English) Zbl 07891423

Scalar BSDEs of iterated-logarithmically sub-linear generators with integrable terminal values. (English) Zbl 07885782

Enhancing physics informed neural networks for solving Navier-Stokes equations. (English) Zbl 07882704

Caputo fractional backward stochastic differential equations driven by fractional Brownian motion with delayed generator. (English) Zbl 1541.60040

One dimensional BSDEs with critical integrable terminal values and infinite time horizon. (English) Zbl 07878490

Optimal control for both forward and backward discrete-time systems. (English) Zbl 07875915

Richardson extrapolation of the Crank-Nicolson scheme for backward stochastic differential equations. (English) Zbl 07874382

Exact controllability for mean-field type linear game-based control systems. (English) Zbl 1540.60107

Markovian quadratic BSDEs with an unbounded sub-quadratic growth. (English) Zbl 1540.60115

PDE-based Bayesian inference of CEV dynamics for credit risk in stock prices. (English) Zbl 07872898

Numerical approximation based on deep convolutional neural network for high-dimensional fully nonlinear merged PDEs and 2BSDEs. (English) Zbl 07869373

Dynamic programming principle for one kind of stochastic recursive optimal control problem with Markovian switching. (English) Zbl 07866366

Reflected backward stochastic differential equations driven by \(G\)-Brownian motion under monotonicity condition. (English) Zbl 07865989

Reflected and doubly reflected backward stochastic differential equations with irregular obstacles and a large set of stopping strategies. (English) Zbl 07865962

Doubly reflected generalized BSDEs with jumps and an obstacle problem of parabolic IPDEs with nonlinear Neumann boundary conditions. (English) Zbl 1540.60111

A gradient method for high-dimensional BSDEs. (English) Zbl 07864355

Picard approximation of a singular backward stochastic nonlinear Volterra integral equation. (English) Zbl 07859967

Dynamic capital allocation rules via BSDEs: an axiomatic approach. (English) Zbl 1537.91360

Reflections on BSDEs. (English) Zbl 07854763

Optimal control of stochastic delay differential equations and applications to path-dependent financial and economic models. (English) Zbl 07854558

Forward-backward stochastic evolution equations in infinite dimensions and application to LQ optimal control problems. (English) Zbl 1537.93337

Reflected BSDEs driven by \(G\)-Brownian motion with time-varying Lipschitz coefficients. (English) Zbl 1537.60069

Doubly reflected BSDEs driven by RCLL martingales under stochastic Lipschitz coefficient. (English) Zbl 1537.60067

Multi-stage Euler-Maruyama methods for backward stochastic differential equations driven by continuous-time Markov chains. (English) Zbl 1536.60058

Linear-quadratic stochastic Stackelberg games of \(N\) players for time-delay systems and related FBSDEs. (English) Zbl 1536.91043

Weak compactness of weak solutions sets of forward-backward stochastic differential inclusions. (English) Zbl 1535.60100

A mild approach to spatial discretization for backward stochastic differential equations in infinite dimensions. (English) Zbl 07834379

Wellposedness of anticipated BSDEs with quadratic growth and unbounded terminal value. (English) Zbl 1534.60077

Consumption and portfolio optimization with generalized stochastic differential utility in incomplete markets. (English) Zbl 1536.91303

Optimal investment in a large population of competitive and heterogeneous agents. (English) Zbl 1533.91435

Stochastic maximum principle for subdiffusions and its applications. (English) Zbl 1539.93205

On Z-mean reflected BSDEs. (English) Zbl 07824112

On mean-field control problems for backward doubly stochastic systems. (English) Zbl 1533.93851

Well-posedness and regularity of mean-field backward doubly stochastic Volterra integral equations and applications to dynamic risk measures. (English) Zbl 1532.60133

Time-delayed generalized BSDEs. (English) Zbl 07812485

Stochastic controls of fractional Brownian motion. (English) Zbl 1533.93842

Backward doubly stochastic differential equations driven by fractional Brownian motion with stochastic integral-Lipschitz coefficients. (English) Zbl 07812407

Deep learning algorithms for solving high-dimensional nonlinear backward stochastic differential equations. (English) Zbl 1532.60153

Wellposedness of second order reflected BSDEs: a new formulation. (English) Zbl 07806691

Sequential propagation of chaos for mean-field BSDE systems. (English) Zbl 1534.65027

Multi-dimensional mean-reflected BSDEs driven by \(G\)-Brownian motion with time-varying non-Lipschitz coefficients. (English) Zbl 1532.60121

Existence and uniqueness of solution for fully coupled fractional forward-backward stochastic differential equations with delay and anticipated term. (English) Zbl 1534.34074

Invariant representation for generators of general time interval quadratic BSDEs under stochastic growth conditions. (English) Zbl 1532.60135

A generalized finite element \(\theta\)-scheme for backward stochastic partial differential equations and its error estimates. (English) Zbl 1531.65179

Generalized BSDEs driven by RCLL martingales with stochastic monotone coefficients. (English) Zbl 1535.60097

A mathematical perspective of machine learning. (English) Zbl 1535.68258

Risk-sensitive stochastic maximum principle for forward-backward systems involving Impulse controls. (English) Zbl 1533.93854

ODE-based multistep schemes for backward stochastic differential equations. (English) Zbl 07814777

Viscosity solutions to second order path-dependent Hamilton-Jacobi-Bellman equations and applications. (English) Zbl 07791542

Dynamic programming approach to reflected backward stochastic differential equations. (English) Zbl 07790277

Backward stochastic evolution inclusions in UMD Banach spaces. (English) Zbl 1528.60058