Articlebronze2013

Second order reflected backward stochastic differential equations

39 citations0/0 files storedThe Annals of Applied Probability

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Stochastic processes and financial applications Risk and Portfolio Optimization Fuzzy Systems and Optimization

Abstract

In this article, we build upon the work of Soner, Touzi and Zhang [Probab. Theory Related Fields 153 (2012) 149–190] to define a notion of a second order backward stochastic differential equation reflected on a lower càdlàg obstacle. We prove existence and uniqueness of the solution under a Lipschitz-type assumption on the generator, and we investigate some links between our reflected 2BSDEs and nonclassical optimal stopping problems. Finally, we show that reflected 2BSDEs provide a super-hedging price for American options in a market with volatility uncertainty.

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References

1990Adapted solution of a backward stochastic differential equation 1997Reflected solutions of backward SDE's, and related obstacle problems for PDE's 1995Pricing and hedging derivative securities in markets with uncertain volatilities 2019Nonlinear Expectations and Stochastic Calculus under Uncertainty 2006A theoretical framework for the pricing of contingent claims in the presence of model uncertainty 1999Monotonic limit theorem of BSDE and nonlinear decomposition theorem of Doob–Meyers type 2011Wellposedness of second order backward SDEs 2006Second‐order backward stochastic differential equations and fully nonlinear parabolic PDEs

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