scholarly journals Backward stochastic differential equations with singular terminal condition

2006 ◽  
Vol 116 (12) ◽  
pp. 2014-2056 ◽  
Author(s):  
A. Popier
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Backward Stochastic Differential Equations ◽  
Terminal Condition

A Monte Carlo method for backward stochastic differential equations with Hermite martingales

2019 ◽  
Vol 25 (1) ◽  
pp. 37-60
Author(s):  
Antoon Pelsser ◽  
Kossi Gnameho
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Numerical Approximation ◽  
Mathematical Finance ◽  
Backward Stochastic Differential Equations ◽  
Terminal Condition ◽  
Dimensional System ◽  
Infinite Dimensional ◽  
The Family ◽  
Infinite Dimensional System

Abstract Backward stochastic differential equations (BSDEs) appear in many problems in stochastic optimal control theory, mathematical finance, insurance and economics. This work deals with the numerical approximation of the class of Markovian BSDEs where the terminal condition is a functional of a Brownian motion. Using Hermite martingales, we show that the problem of solving a BSDE is identical to solving a countable infinite-dimensional system of ordinary differential equations (ODEs). The family of ODEs belongs to the class of stiff ODEs, where the associated functional is one-sided Lipschitz. On this basis, we derive a numerical scheme and provide numerical applications.

Path-dependent BSDEs with jumps and their connection to PPIDEs

2016 ◽  
Vol 17 (05) ◽  
pp. 1750036 ◽  
Author(s):  
Eduard Kromer ◽  
Ludger Overbeck ◽  
Jasmin A. L. Röder
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Viscosity Solution ◽  
Path Dependence ◽  
Backward Stochastic Differential Equations ◽  
Terminal Condition ◽  
Path Dependent

We study path-dependent backward stochastic differential equations (BSDEs) with jumps. In this context path-dependence of a BSDE is the dependence of the BSDE-terminal condition and the BSDE-generator of a path of a càdlàg process. We study the path-differentiability of BSDEs of this type and establish a connection to path-dependent PIDEs in terms of the existence of a viscosity solution and the respective Feynman–Kac theorem.

DISSIPATIVE BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS IN INFINITE DIMENSIONS

2006 ◽  
Vol 09 (01) ◽  
pp. 155-168 ◽  
Author(s):  
FULVIA CONFORTOLA
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Hilbert Spaces ◽  
Stochastic Partial Differential Equations ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equations ◽  
Uniqueness Result ◽  
Infinite Dimensions ◽  
Partial Differential

We prove an existence and uniqueness result for a class of backward stochastic differential equations (BSDE) with dissipative drift in Hilbert spaces. We also give examples of stochastic partial differential equations which can be solved with our result.

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