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3 matches found
XII: 33, 457-467, LNM 649 (1978)
Temps d'arrêt optimaux et théorie générale (General theory of processes)
This is a general discussion of optimal stopping in continuous time. Fairly advanced tools like strong supermartingales, Mertens' decomposition are used
Comment: The subject is taken up in 1332
Keywords: Optimal stopping, Snell's envelope
Nature: Original
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XIII: 32, 378-384, LNM 721 (1979)
Théorème de séparation dans le problème d'arrêt optimal (General theory of processes)
Let $({\cal G}_t)$ be an enlargement of a filtration $({\cal F}_t)$ with the property that for every $t$, if $X$ is ${\cal G}_t$-measurable, then $E[X\,|\,{\cal F}_t]=E[X\,|\,{\cal F}_\infty]$. Then if $(X_t)$ is a ${\cal F}$-optional process, its Snell envelope is the same in both filtrations. Applications are given to filtering theory
Keywords: Optimal stopping, Snell's envelope, Filtering theory
Nature: Original
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XV: 24, 320-346, LNM 850 (1981)
Sur des problèmes de régularisation, de recollement et d'interpolation en théorie des martingales (General theory of processes)
The optional section theorem implies that an optional process $X$ is completely determined by its values $X_T$ at all stopping times. Conversely, given random variables $X_T$, ${\cal F}_T$-measurable and such that $X_S=X_T$ a.s. on the set $\{S=T\}$, is it possible to ``aggregate'' them into an optional process $X$? This is the elementary form of the general problem discussed in the paper, in the case where the random variables $X_T$ satisfy a supermartingale inequality. The problem solved is more general: the optional $\sigma$-field is replaced by any of the $\sigma$-fields considered in 1449 (including previsible, accessible, etc), and the family of all stopping times is replaced by a suitable family (called a chronology)
Keywords: General filtrations, Strong supermartingales, Snell's envelope, Section theorems
Nature: Original
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