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- W4226052216 abstract "In the present paper we address stochastic optimal control problems for a step process $(X,mathbb{F})$ under a progressive enlargement of the filtration. The global information is obtained adding to the reference filtration $mathbb{F}$ the point process $H=1_{[tau,+infty)}$. Here $tau$ is a random time that can be regarded as the occurrence time of an external shock event. We study two classes of control problems, over $[0,T]$ and over the random horizon $[0,T wedge tau]$. We solve these control problems following a dynamical approach based on a class of BSDEs driven by the jump measure $mu^ Z$ of the semimartingale $Z=(X,H)$, which is a step process with respect to the enlarged filtration $mathbb G$. The BSDEs that we consider can be solved in $mathbb{G}$ thanks to a martingale representation theorem which we also establish here. To solve the BSDEs and the control problems we need to ensure that $Z$ is quasi-left continuous in the enlarged filtration $mathbb{G}$. Therefore, in addition to the $mathbb{F}$-quasi left continuity of $X$, we assume some further conditions on $tau$: the {it avoidance} of $mathbb{F}$-stopping times and the {it immersion} property, or alternatively {it Jacod's absolutely continuity} hypothesis." @default.
- W4226052216 created "2022-05-05" @default.
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- W4226052216 date "2021-12-23" @default.
- W4226052216 modified "2023-09-26" @default.
- W4226052216 title "Progressively Enlargement of Filtrations and Control Problems for Step Processes" @default.
- W4226052216 doi "https://doi.org/10.48550/arxiv.2112.12884" @default.
- W4226052216 hasPublicationYear "2021" @default.
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