Lower bounds of martingale measure densities in the Dalang-Morton-Willinger theorem

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dc.creatorRokhlin, Dmitry B.
dc.date2008-04-10
dc.date.accessioned2026-07-07T09:31:36Z
dc.date.available2026-07-07T09:31:36Z
dc.descriptionFor a $d$-dimensional stochastic process $(S_n)_{n=0}^N$ we obtain criteria for the existence of an equivalent martingale measure, whose density $z$, up to a normalizing constant, is bounded from below by a given random variable $f$. We consider the case of one-period model (N=1) under the assumptions $S\in L^p$; $f,z\in L^q$, $1/p+1/q=1$, where $p\in [1,\infty]$, and the case of $N$-period model for $p=\infty$. The mentioned criteria are expressed in terms of the conditional distributions of the increments of $S$, as well as in terms of the boundedness from above of an utility function related to some optimal investment problem under the loss constraints. Several examples are presented.
dc.description19 pages
dc.identifierhttps://arxiv.org/abs/0804.1761
dc.identifierhttp://arxiv.org/abs/0804.1761
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/158518
dc.subjectProbability
dc.subject60G42, 91B24, 91B28
dc.titleLower bounds of martingale measure densities in the Dalang-Morton-Willinger theorem
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