Reflected BSDEs with monotone generator

Tomasz Klimsiak

38 citations0/0 files storedElectronic Journal of Probability

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

Abstract

We give necessary and sufficient condition for existence and uniqueness of $\mathbb{L}^{p}$-solutions of reflected BSDEs with continuous barrier, generator monotone with respect to $y$ and Lipschitz continuous with respect to $z$, and with data in $\mathbb{L}^{p}$, $p\ge 1$. We also prove that the solutions maybe approximated by the penalization method.

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References

1997Reflected solutions of backward SDE's, and related obstacle problems for PDE's 1981Les Aspects Probabilistes Du Controle Stochastique 2003Lp solutions of backward stochastic differential equations 1999Monotonic limit theorem of BSDE and nonlinear decomposition theorem of Doob–Meyers type 1996Backward stochastic differential equations with reflection and Dynkin games 1997Reflected Backward SDEs and American Options 2005The smallest g-supermartingale and reflected BSDE with single and double L2L2 obstacles 1997Reflected solutions of backward stochastic differential equations with continuous coefficient

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