14h30
Christophe CHORRO (Paris 1).
GARCH option pricing models.
15h30 Pause café et
discussions.
16h00 Anis MATOUSSI (Le Mans et CMAP)
Second
order reflected BSDE's and applications for stochastic control and game
under uncertainty.
Abstract.
We present results
concerning the existence and uniqueness
of second-order reflected BSDEs, developed in [1] and [2]. In
particular,
in the case of
reflection with two 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 Cvitani\'c 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.
References :
[1] A. Matoussi, D. Possamai and
C. Zhou. Second Order Reflected BSDE's. arXiv:1201.0746 (2012). The
Ann. of App. Probab., to appear.
[2] A. Matoussi,
L. Piozin and D. Possamai. Second-order BSDEs with general reflection
and Dynkin games under uncertainty. arXiv:1201:0746v2 (2012).
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