Abstract
First we consider a set of probabilities and denote by
, the associated dynamic sublinear expectation, defined by
for
and a fixed filtration
. We prove that for a positive
-supermartingale X, there exits an increasing adapted process C such that
is a local
-martingale. Second we apply such a result to incomplete market under model misspecification, generalizing the results of Kramkov [D.O. Kramkov, Optional decomposition of supermartingales and hedging contingent claims in incomplete security markets, Prob. Theor. Relat. Field. 15 (1996), pp. 459–479] and Riedel [F. Riedel, On optimal stopping under Ambiguity, Econometrica. 77 (2009), pp. 857–908].
AMS Subject Classification::
Acknowledgements
The author thanks the associate editor and the two referees for their useful comments which improved this work.