A Doob-Meyer decomposition under model ambiguity: the case of compactness

Erick Treviño-Aguilar
2021 Latin American Journal of Probability and Mathematical Statistics  
We consider families of equivalent probability measures Q with a property related to concepts known in the literature under different names such as rectangularity or multiplicative stability. For the problems considered in this paper such a property yields dynamical consistency. We prove under a weak-compactness assumption with general filtrations and continuous processes that all semimartingales have an additive decomposition as the sum of a predictable non-decreasing process and a universal
more » ... s and a universal local supermartingale, by this concept we mean a process that is a local supermartingale with respect to each element of Q. We also show that processes having a supermartingale property with respect to a superadditive nonlinear conditional expectation associated to the family Q are always semimartingales under weak-compactness. These results are relevant in stochastic optimization problems including optimal stopping under model ambiguity.
doi:10.30757/alea.v18-24 fatcat:chkbf3bgbngrdm5rzgead5chq4