Backward stochastic differential equations and partial differential equations with quadratic growth

2000-04-01articleThe Annals of Probability763 citationsclosed

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Stochastic processes and financial applications Nonlinear Partial Differential Equations Fuzzy Systems and Optimization

Abstract

We provide existence, comparison and stability results for one- dimensional backward stochastic differential equations (BSDEs) when the coefficient (or generator) $F(t,Y, Z)$ is continuous and has a quadratic growth in $Z$ and the terminal condition is bounded.e also give, in this framework, the links between the solutions of BSDEs set on a diffusion and viscosity or Sobolev solutions of the corresponding semilinear partial differential equations.

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References

1990Adapted solution of a backward stochastic differential equation

1997Backward Stochastic Differential Equations in Finance

2005Backward stochastic differential equations and quasilinear parabolic partial differential equations

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