Backward doubly stochastic Volterra integral equations and their applications

DOI10.1016/j.jde.2020.05.006zbMath1443.60056OpenAlexW3033321365MaRDI QIDQ2189775

Jiaqiang Wen, Jie Xiong, Yu-feng Shi

Publication date: 16 June 2020

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2020.05.006

zbMATH Keywords

comparison theoremPontryagin maximum principleduality principlebackward doubly stochastic Volterra integral equations

Mathematics Subject Classification ID

Optimal stochastic control (93E20) Stochastic integrals (60H05) Stochastic integral equations (60H20)

Related Items (13)

Doubly-stochastic interpretation for nonlocal semi-linear backward stochastic partial differential equations ⋮ Anticipated backward stochastic Volterra integral equations with jumps and applications to dynamic risk measures ⋮ Mean-field backward doubly stochastic Volterra integral equations and their applications ⋮ Well-posedness and regularity of mean-field backward doubly stochastic Volterra integral equations and applications to dynamic risk measures ⋮ Forward-backward doubly stochastic systems and classical solutions of path-dependent stochastic PDEs ⋮ Extended backward stochastic Volterra integral equations and their applications to time-inconsistent stochastic recursive control problems ⋮ Mean-field type forward-backward doubly stochastic differential equations and related stochastic differential games ⋮ A unified approach to well-posedness of type-I backward stochastic Volterra integral equations ⋮ Mean-field backward stochastic differential equations driven by fractional Brownian motion ⋮ Weak closed-loop solvability of stochastic linear quadratic optimal control problems of Markovian regime switching system ⋮ Some results on backward stochastic differential equations of fractional order ⋮ Backward stochastic differential equations and backward stochastic Volterra integral equations with anticipating generators ⋮ Variation of constants formulae for forward and backward stochastic Volterra integral equations

Cites Work

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• Mean-field backward stochastic Volterra integral equations
• Backward stochastic differential equations with rough drivers
• Adapted solution of a backward stochastic differential equation
• Well-posedness and regularity of backward stochastic Volterra integral equations
• Forward-backward stochastic differential equations and their applications
• Backward doubly stochastic differential equations and systems of quasilinear SPDEs
• Backward stochastic differential equations with continuous coefficient
• A type of time-symmetric forward-backward stochastic differential equations
• Linear Volterra backward stochastic integral equations
• Super-Brownian motion as the unique strong solution to an SPDE
• Symmetrical martingale solutions of backward doubly stochastic Volterra integral equations
• Mean-field anticipated BSDEs driven by fractional Brownian motion and related stochastic control problem
• Comparison theorems for some backward stochastic Volterra integral equations
• Weak closed-loop solvability of stochastic linear quadratic optimal control problems of Markovian regime switching system
• Backward stochastic Volterra integral equations -- representation of adapted solutions
• Path-dependent backward stochastic Volterra integral equations with jumps, differentiability and duality principle
• Optimal control problems of forward-backward stochastic Volterra integral equations
• Generalized backward doubly stochastic differential equations and SPDEs with nonlinear Neumann boundary conditions
• Backward stochastic Volterra integral equations and some related problems
• Risk measures via \(g\)-expectations
• Backward doubly stochastic differential equations with random coefficients and quasilinear stochastic PDEs
• Coherent Measures of Risk
• Discretization of backward stochastic Volterra integral equations
• Regularity of Backward Stochastic Volterra Integral Equations in Hilbert Spaces
• Maximum Principle for Backward Doubly Stochastic Control Systems with Applications
• Continuous-time dynamic risk measures by backward stochastic Volterra integral equations
• Backward Stochastic Differential Equations in Finance
• Adapted solution of a backward stochastic nonlinear Volterra integral equation
• DIFFERENTIABILITY OF BSVIEs AND DYNAMIC CAPITAL ALLOCATIONS
• Comparison Theorems of Backward Doubly Stochastic Differential Equations and Applications
• SOLVABILITY OF GENERAL BACKWARD STOCHASTIC VOLTERRA INTEGRAL EQUATIONS
• New approach to optimal control of stochastic Volterra integral equations
• Optimal Control Problems of Forward-Backward Stochastic Volterra Integral Equations with Closed Control Regions

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