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- Title
On the compensator of step processes in progressively enlarged filtrations and related control problems.
- Authors
Bandini, Elena; Confortola, Fulvia; Di Tella, Paolo
- Abstract
For a step process X with respect to its natural filtration F, we denote by G the smallest right-continuous filtration containing F and such that another step process H is adapted. We investigate some structural properties of the step process X in G. We show that Z =(X,H) possesses the weak representation property with respect to G. Moreover, in the case H = 1[t,+8), where t is a random time (but not an F-stopping time) satisfying Jacod's absolute continuity hypothesis, we compute the G-predictable compensator vG,X of the jump measure of X. Thanks to our theoretical results on vG,X, we can consider stochastic control problems related to model uncertainty on the intensity measure of X, also in presence of an external risk source modeled by the random time t.
- Subjects
COMPENSATORY balances; STOCHASTIC analysis; STATISTICAL hypothesis testing; FILTERS &; filtration; MATHEMATICS
- Publication
ALEA. Latin American Journal of Probability & Mathematical Statistics, 2024, Vol 21, Issue 1, p95
- ISSN
1980-0436
- Publication type
Article
- DOI
10.30757/ALEA.v21-05