The Annals of Applied Probability

Second order reflected backward stochastic differential equations

Anis Matoussi, Dylan Possamai, and Chao Zhou

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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.

Article information

Source
Ann. Appl. Probab., Volume 23, Number 6 (2013), 2420-2457.

Dates
First available in Project Euclid: 22 October 2013

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1382447693

Digital Object Identifier
doi:10.1214/12-AAP906

Mathematical Reviews number (MathSciNet)
MR3127940

Zentralblatt MATH identifier
1303.60049

Subjects
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05] 60H30: Applications of stochastic analysis (to PDE, etc.)

Keywords
Second order backward stochastic differential equation reflected backward stochastic differential equation

Citation

Matoussi, Anis; Possamai, Dylan; Zhou, Chao. Second order reflected backward stochastic differential equations. Ann. Appl. Probab. 23 (2013), no. 6, 2420--2457. doi:10.1214/12-AAP906. https://projecteuclid.org/euclid.aoap/1382447693


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