Results 1 to 10 of about 61,087 (328)

Linear Forward—Backward Stochastic Differential Equations [PDF]

Applied Mathematics and Optimization, 1999
Theorems are proved establishing conditions for the solvability of a system of coupled linear forward-backward stochastic differential equations of the form \[ dX(t)= \bigl\{AX(t)+BY(t) +CZ(t)+Db(t)\bigr\}dt +\bigl \{A_1X(t) +B_1Y(t)+ C_1Z(t)+ D_1\sigma (t)\bigr\}dW(t), \] \[ dY(t)= \bigl\{ \widehat AX(t)+ \widehat BY(t)+ \widehat CZ(t)+ \widehat D ...
openaire   +1 more source

Generalized BDSDEs driven by fractional Brownian motion

Nonautonomous Dynamical Systems, 2023
This article deals with a class of generalized backward doubly stochastic differential equations driven by fractional Brownian motion with the Hurst parameter HH greater than 1/2.
Aidara Sadibou, Ndiaye Assane, Sow Ahmadou Bamba   +2 more
doaj   +1 more source

Differentiability of backward stochastic differential equations in Hilbert spaces with monotone generators [PDF]

, 2006
The aim of the present paper is to study the regularity properties of the solution of a backward stochastic differential equation with a monotone generator in infinite dimension.
A. Bensoussan, A. Bensoussan, E. Pardoux, E. Pardoux, E. Pardoux, E. Pardoux, F. Gozzi, Fulvia Confortola, G. Da Prato, J. Ma, J. Zabczyk, M. Fuhrman, M. Fuhrman, N. El Karoui, N. El Karoui, Ph. Briand, Philippe Briand, S. Cerrai, S. Peng, S. Peng, S. Peng, S. Peng, W.H. Fleming   +22 more
core   +5 more sources

Backward-Forward Stochastic Differential Equations

The Annals of Applied Probability, 1993
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

Backward Stochastic Differential Equations (BSDEs) Using Infinite-Dimensional Martingales with Subdifferential Operator

Axioms, 2022
In this paper, we focus on a family of backward stochastic differential equations (BSDEs) with subdifferential operators that are driven by infinite-dimensional martingales. We shall show that the solution to such infinite-dimensional BSDEs exists and is
Pei Zhang, Adriana Irawati Nur Ibrahim, Nur Anisah Mohamed   +2 more
doaj   +1 more source

Penalization method for a nonlinear Neumann PDE via weak solutions of reflected SDEs

, 2013
In this paper we prove an approximation result for the viscosity solution of a system of semi-linear partial differential equations with continuous coefficients and nonlinear Neumann boundary condition. The approximation we use is based on a penalization
Bahlali, Khaled, Maticiuc, Lucian, Zalinescu, Adrian   +2 more
core   +3 more sources

Semi-linear degenerate backward stochastic partial differential equations and associated forward–backward stochastic differential equations

Stochastic Processes and their Applications, 2013
23 ...
Du, Kai, Zhang, Qi
openaire   +4 more sources

Stochastic Maximum Principle for Optimal Control ofPartial Differential Equations Driven by White Noise

, 2017
We prove a stochastic maximum principle ofPontryagin's type for the optimal control of a stochastic partial differential equationdriven by white noise in the case when the set of control actions is convex.
Fuhrman, Marco, Hu, Ying, Tessitore, Gianmario   +2 more
core   +3 more sources

Hybrid Neural Networks for Solving Fully Coupled, High-Dimensional Forward–Backward Stochastic Differential Equations

Mathematics
The theory of forward–backward stochastic differential equations occupies an important position in stochastic analysis and practical applications. However, the numerical solution of forward–backward stochastic differential equations, especially for high ...
Mingcan Wang, Xiangjun Wang
doaj   +1 more source

Study of Pricing of High-Dimensional Financial Derivatives Based on Deep Learning

Mathematics, 2023
Many problems in the fields of finance and actuarial science can be transformed into the problem of solving backward stochastic differential equations (BSDE) and partial differential equations (PDEs) with jumps, which are often difficult to solve in high-
Xiangdong Liu, Yu Gu
doaj   +1 more source