Backward stochastic differential equations with a uniformly continuous generator and related \(g\)-expectation

DOI10.1016/j.spa.2010.06.006zbMath1204.60051OpenAlexW2078206086MaRDI QIDQ607277

Guangyan Jia

Publication date: 19 November 2010

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.spa.2010.06.006

zbMATH Keywords

uniquenessbackward stochastic differential equationuniform continuitystrict monotonicityg-expectation

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10)

Related Items (15)

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Cites Work

• Unnamed Item
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• Adapted solution of a backward stochastic differential equation
• Quadratic BSDEs with convex generators and unbounded terminal conditions
• Representation theorems for quadratic \(\mathcal F\)-consistent nonlinear expectations
• Backward stochastic differential equations: The locally Lipschitz case
• Backward stochastic differential equations with continuous coefficient
• Jensen's inequality for \(g\)-expectation. I
• A converse comparison theorem for BSDEs and related properties of \(g\)-expectation
• On Jensen's inequality for \(g\)-expectation
• Filtration-consistent nonlinear expectations and related \(g\)-expectations
• Backward stochastic differential equations and partial differential equations with quadratic growth.
• Jensen's inequality for \(g\)-convex function under \(g\)-expectation
• A uniqueness theorem for the solution of backward stochastic differential equations
• BSDE with quadratic growth and unbounded terminal value
• Risk measures via \(g\)-expectations
• Representation theorems for generators of backward stochastic differential equations and their applications
• On Jensen's inequality for \(g\)-expectation and for nonlinear expectation
• A Generalized dynamic programming principle and hamilton-jacobi-bellman equation
• A property of backward stochastic differential equations
• Backward Stochastic Differential Equations in Finance
• Ambiguity, Risk, and Asset Returns in Continuous Time

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