Second-order BSDEs with general reflection and game options under uncertainty

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:124

Article

Matoussi, Anis^1,2,3  Piozin, Lambert²  Possamai, Dylan⁴ 

[1] Univ Maine, LUNAM Univ, Fed Rech CNRS 2962, F-72085 Le Mans 9, France

[2] Lab Manceau Math, F-72085 Le Mans 9, France

[3] Ecole Polytech, CMAP, Palaiseau, France

[4] Univ Paris 09, CEREMADE, Bur B518, F-75775 Paris 16, France

关键词: Second order backward stochastic differential equation;    Reflected backward stochastic differential equation;    Dynkin games;    Israeli options;    Volatility uncertainty;   

DOI  :  10.1016/j.spa.2014.02.011

来源: Elsevier

【 摘 要 】

The aim of this paper is twofold. First, we extend the results of Matoussi et al. (2013) concerning the existence and uniqueness of second-order reflected 2BSDEs to the case of two obstacles. Under some regularity assumptions on one of the barriers, similar to the ones in Crepey and Matoussi (2008), and when the two barriers are completely separated, 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 Cvitanic and Karatzas (1996). More precisely, we show under a technical assumption 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. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free