Abstract:

We study the existence and uniqueness of second-order reflected 2BSDEs with one and two obstacles. For the later one, under some regularity assumptions on one of the barriers, we provide a complete wellposedness theory for doubly reflected second-order BSDEs. We also show that these objects are related to non-standard optimal stopping games, thus generalizing the connection between DRBSDEs and Dynkin games first proved by Cvitanić and Karatzas (1996). More precisely, we show that the second order DRBSDEs provide solutions of what we call uncertain Dynkin games and that they also allow us to obtain super and subhedging prices for American game options (also called Israeli options) in financial markets with volatility uncertainty.  This talk is based on the following two papers:

[1] A. Matoussi, D. Possamai and C. Zhou. Second Order Reflected BSDE. The Annals of Applied Probability, Volume 23, Number 6 (2013), 2161-2603.

[2]  A. Matoussi, L. Piozin, D. Possamai. Second-order BSDEs with general reflection and Dynkin games under uncertainty.Prépublication 2012, arXiv:1212.0476 (2012), Stochastic Processes and Their Applications, Vol. 124, Issue 7, 2281–2321 (2014).