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BSDEs with diffusion constraint and viscous Hamilton-Jacobi equations with unbounded data

Cosso, Andrea, Pham, Huyên and Xing, Hao (2017) BSDEs with diffusion constraint and viscous Hamilton-Jacobi equations with unbounded data. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 53 (4). pp. 1528-1547. ISSN 0246-0203

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Identification Number: 10.1214/16-AIHP762

Abstract

We provide a stochastic representation for a general class of viscous Hamilton-Jacobi (HJ) equations, which has convex and superlinear nonlinearity in its gradient term, via a type of backward stochastic differential equation (BSDE) with constraint in the martingale part. We compare our result with the classical representation in terms of (super)quadratic BSDEs, and show in particular that existence of a viscosity solution to the viscous HJ equation can be obtained under more general growth assumptions on the coefficients, including both unbounded diffusion coefficient and terminal data.

Item Type: Article
Official URL: http://www.imstat.org/aihp/default.htm
Additional Information: © 2017 Association des Publications de l’Institut Henri Poincaré
Divisions: Statistics
Subjects: Q Science > QA Mathematics
Sets: Departments > Statistics
Date Deposited: 31 Jan 2017 15:03
Last Modified: 20 Oct 2020 05:14
URI: http://eprints.lse.ac.uk/id/eprint/69156

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