Lp-SOLUTIONS FOR REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS

Saïd Hamadène · Alexandre Popier

39 citations0/0 files storedStochastics and Dynamics

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

Abstract

This paper deals with the problem of existence and uniqueness of a solution for a backward stochastic differential equation (BSDE for short) with one reflecting barrier in the case when the terminal value, the generator and the obstacle process are Lp-integrable with p ∈ ]1, 2[. To construct the solution we use two methods: penalization and Snell envelope. As an application we broaden the class of functions for which the related obstacle partial differential equation problem has a unique viscosity solution.

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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 1997Reflected solutions of backward SDE's, and related obstacle problems for PDE's 1997Backward stochastic differential equations and integral-partial differential equations 2000Pricing Via Utility Maximization and Entropy 1981Les Aspects Probabilistes Du Controle Stochastique 2003Lp solutions of backward stochastic differential equations

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2013Second order reflected backward stochastic differential equations 2015Reflected BSDEs on filtered probability spaces 2012Reflected BSDEs with monotone generator 2018Reflected BSDEs with regulated trajectories 2012Lp solutions of reflected BSDEs under monotonicity condition

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