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

Andrea Cosso; Huyên Pham; Hao Xing

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arXiv · 1505.06868

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

Andrea Cosso·Huyên Pham·Hao Xing

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Abstract

We provide a stochastic representation for a general class of viscous Hamilton-Jacobi (HJ) equations, which has convexity 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 BSDE, and show in particular that existence of a 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.

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Andrea Cosso, Huyên Pham, Hao Xing. 2015-05-26. BSDEs with diffusion constraint and viscous Hamilton-Jacobi equations with unbounded data. https://arxiv.org/abs/1505.06868

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