Pathwise inequalities for local time: Applications to Skorokhod embeddings and optimal stopping

Simple item page
dc.creatorCox, A. M. G.
dc.creatorHobson, David
dc.creatorObłój, Jan
dc.date2007-02-07
dc.date2008-11-13
dc.date.accessioned2026-07-07T12:07:21Z
dc.date.available2026-07-07T12:07:21Z
dc.descriptionWe develop a class of pathwise inequalities of the form $H(B_t)\ge M_t+F(L_t)$, where $B_t$ is Brownian motion, $L_t$ its local time at zero and $M_t$ a local martingale. The concrete nature of the representation makes the inequality useful for a variety of applications. In this work, we use the inequalities to derive constructions and optimality results of Vallois' Skorokhod embeddings. We discuss their financial interpretation in the context of robust pricing and hedging of options written on the local time. In the final part of the paper we use the inequalities to solve a class of optimal stopping problems of the form $\sup_τ\mathbb{E}[F(L_τ)-\int _0^τβ(B_s) ds]$. The solution is given via a minimal solution to a system of differential equations and thus resembles the maximality principle described by Peskir. Throughout, the emphasis is placed on the novelty and simplicity of the techniques.
dc.descriptionPublished in at http://dx.doi.org/10.1214/07-AAP507 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0702173
dc.identifierhttp://arxiv.org/abs/math/0702173
dc.identifierAnnals of Applied Probability 2008, Vol. 18, No. 5, 1870-1896
dc.identifierdoi:10.1214/07-AAP507
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/208941
dc.subjectProbability
dc.subjectPricing of Securities
dc.subject60G40 (Primary) 60G44, 91B28 (Secondary)
dc.titlePathwise inequalities for local time: Applications to Skorokhod embeddings and optimal stopping
dc.typetext

Files

Collections

arXiv