A Doob-Meyer decomposition under model ambiguity: the case of compactness
Por:
Treviño-Aguilar E.
Publicada:
1 ene 2021
Categoría:
Statistics and probability
Resumen:
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 semimartin-gales have an
additive decomposition as the sum of a predictable non-decreasing
process 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.
Filiaciones:
Treviño-Aguilar E.:
Instituto de Matemáticas, Unidad Cuernavaca, Universidad Nacional Autónoma de México, Av. Universidad s/n, Cuernavaca, Morelos CP 62210, Mexico
Bronze
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