Results 11 to 20 of about 3,305 (167)

Closed-Loop Solvability of Stochastic Linear-Quadratic Optimal Control Problems with Poisson Jumps

Mathematics, 2022
The stochastic linear–quadratic optimal control problem with Poisson jumps is addressed in this paper. The coefficients in the state equation and the weighting matrices in the cost functional are all deterministic but are allowed to be indefinite.
Zixuan Li, Jingtao Shi
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Backward stochastic differential equations and backward stochastic Volterra integral equations with anticipating generators

Probability, Uncertainty and Quantitative Risk, 2022
For a backward stochastic differential equation (BSDE, for short), when the generator is not progressively measurable, it might not admit adapted solutions, shown by an example. However, for backward stochastic Volterra integral equations (BSVIEs, for short), the generators are allowed to be anticipating.
Wang, Hanxiao, Yong, Jiongmin, Zhou, Chao   +2 more
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L2-convergence of Yosida approximation for semi-linear backward stochastic differential equation with jumps in infinite dimension [PDF]

Arab Journal of Mathematical Sciences
Purpose – The main motivation of this paper is to present  the Yosida approximation of a semi-linear backward stochastic differential equation in infinite dimension. Under suitable assumption and condition, an L2-convergence rate is established.
Hani Abidi, Rim Amami, Roger Pettersson, Chiraz Trabelsi   +3 more
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Backward Stochastic Differential Equations [PDF]

, 2015
In this chapter, we consider a different type of stochastic differential equation. In the setting of Chapter 17, we specified a solution process X through its dynamics and its initial value, as in ( 17.6). In this chapter, we specify a solution process Y through its dynamics and its terminal value, at a fixed, deterministic time \(T \in ]0,\infty ...
Samuel N. Cohen, Robert J. Elliott
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Averaging Principle for Backward Stochastic Differential Equations [PDF]

Discrete Dynamics in Nature and Society, 2021
The averaging principle for BSDEs and one-barrier RBSDEs, with Lipschitz coefficients, is investigated. An averaged BSDEs for the original BSDEs is proposed, as well as the one-barrier RBSDEs, and their solutions are quantitatively compared. Under some appropriate assumptions, the solutions to original systems can be approximated by the solutions to ...
Yuanyuan Jing, Zhi Li
openaire   +2 more sources

Maximum principle for a stochastic delayed system involving terminal state constraints

Journal of Inequalities and Applications, 2017
We investigate a stochastic optimal control problem where the controlled system is depicted as a stochastic differential delayed equation; however, at the terminal time, the state is constrained in a convex set.
Jiaqiang Wen, Yufeng Shi
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Discretizing a backward stochastic differential equation

International Journal of Mathematics and Mathematical Sciences, 2002
We show a simple method to discretize Pardoux-Peng's nonlinear backward stochastic differential equation. This discretization scheme also gives a numerical method to solve a class of semi-linear PDEs.
Yinnan Zhang, Weian Zheng
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A direct approach to linear-quadratic stochastic control [PDF]

Opuscula Mathematica, 2017
A direct approach is used to solve some linear-quadratic stochastic control problems for Brownian motion and other noise processes. This direct method does not require solving Hamilton-Jacobi-Bellman partial differential equations or backward stochastic ...
Tyrone E. Duncan, Bozenna Pasik-Duncan
doaj   +1 more source

Harmonic analysis of stochastic equations and backward stochastic differential equations [PDF]

Probability Theory and Related Fields, 2008
The BMO martingale theory is extensively used to study nonlinear multi-dimensional stochastic equations (SEs) in $\cR^p$ ($p\in [1, \infty)$) and backward stochastic differential equations (BSDEs) in $\cR^p\times \cH^p$ ($p\in (1, \infty)$) and in $\cR^\infty\times \bar{\cH^\infty}^{BMO}$, with the coefficients being allowed to be unbounded.
Delbaen, Freddy, Tang, Shanjian
openaire   +3 more sources

Weak Convergence Analysis and Improved Error Estimates for Decoupled Forward-Backward Stochastic Differential Equations

Mathematics, 2021
In this paper, we mainly investigate the weak convergence analysis about the error terms which are determined by the discretization for solving the stochastic differential equation (SDE, for short) in forward-backward stochastic differential equations ...
Wei Zhang, Hui Min
doaj   +1 more source