A representation theorem for generators of BSDEs with continuous linear-growth generators in the space of processes

DOI10.1016/j.cam.2010.06.022zbMath1203.65017OpenAlexW1971709781MaRDI QIDQ708289

Long Jiang, Sheng-Jun Fan

Publication date: 11 October 2010

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2010.06.022

zbMATH Keywords

representation theorembackward stochastic differential equationforward-backward stochastic differential equationgeneralized expectationfinancial mathematicsconverse comparison theoremcontinuous generator

Mathematics Subject Classification ID

Numerical methods (including Monte Carlo methods) (91G60) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Financial applications of other theories (91G80) Ordinary differential equations and systems with randomness (34F05) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)

Related Items (9)

A representation for filtration-consistent nonlinear expectations and its application ⋮ A representation theorem for generators of BSDEs with general growth generators in \(y\) and its applications ⋮ Invariant representation for generators of general time interval quadratic BSDEs under stochastic growth conditions ⋮ On the representation for dynamically consistent nonlinear evaluations: uniformly continuous case ⋮ Representation theorem for generators of quadratic BSDEs ⋮ Representation theorems for generators of BSDEs and the extended \(g\)-expectations in probability spaces with general filtration ⋮ Representation theorems for generators of BSDEs with monotonic and convex growth generators ⋮ Representation theorems of monotonicity generators for BSDEs via L^p (p > 1) solutions in general time intervals ⋮ Viability property for multi-dimensional stochastic differential equation and its applications to comparison theorem

Cites Work

• Adapted solution of a backward stochastic differential equation
• Limit theorem and uniqueness theorem of backward stochastic differential equations
• A limit theorem for solutions to BSDEs in the space of processes
• Quadratic BSDEs with convex generators and unbounded terminal conditions
• Backward stochastic differential equations with continuous coefficient
• Jensen's inequality for \(g\)-expectation. I
• Multidimensional backward stochastic differential equations with uniformly continuous coeffi\-cients
• A converse comparison theorem for BSDEs and related properties of \(g\)-expectation
• Representation theorems for generators of backward stochastic differential equations
• On Jensen's inequality for \(g\)-expectation
• Some results on the uniqueness of generators of backward stochastic differential equations
• Adapted solutions of backward stochastic differential equations with non- Lipschitz coefficients
• A relationship between the conditional \(g\)-evaluation system and the generator \(g\) and its applica\-tions
• Convexity, translation invariance and subadditivity for \(g\)-expectations and related risk measures
• Converse comparison theorems for backward stochastic differential equations
• Backward stochastic differential equations with two reflecting barriers and continuous with quadratic growth coefficient
• \(L^p\) solutions of backward stochastic differential equations.
• Representation theorems for generators of backward stochastic differential equations and their applications
• Backward Stochastic Differential Equations in Finance

This page was built for publication: A representation theorem for generators of BSDEs with continuous linear-growth generators in the space of processes