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dc.contributor.authorEspinosa, Gilles-Edouard
dc.contributor.authorElie, Romuald
dc.date.accessioned2012-07-16T11:35:32Z
dc.date.available2012-07-16T11:35:32Z
dc.date.issued2015
dc.identifier.issn0960-1627
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/9751
dc.language.isoenen
dc.subjectFree boundary PDE
dc.subjectMean reverting diffusion
dc.subjectVerification
dc.subjectRunning maximum
dc.subjectOptimal prediction
dc.subjectOptimal stopping
dc.subject.ddc519en
dc.titleOptimal selling rules for monetary invariant criteria: tracking the maximum of a portfolio with negative drift,
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherDepartement of Mathematics, ETH Zurich;Suisse
dc.contributor.editoruniversityotherCentre de Recherche en Économie et Statistique (CREST) http://www.crest.fr/ INSEE – École Nationale de la Statistique et de l'Administration Économique;France
dc.description.abstractenConsidering a positive portfolio diffusion $X$ with negative drift, we investigate optimal stopping problems of the form $$ \inf_\theta \Esp{f\left(\frac{X_\theta}{\Sup_{s\in[0,\tau]}{X_s}}\right)}\;,$$ where $f$ is a non-increasing function, $\tau$ is the next random time where the portfolio $X$ crosses zero and $\theta$ is any stopping time smaller than $\tau$. Hereby, our motivation is the obtention of an optimal selling strategy minimizing the relative distance between the liquidation value of the portfolio and its highest possible value before it reaches zero. This paper unifies optimal selling rules observed for quadratic absolute distance criteria with bang-bang type ones. More precisely, we provide a verification result for the general stopping problem of interest and derive the exact solution for two classical criteria $f$ of the literature. For the power utility criterion $f:y \mapsto - {y^\la}$ with $\la>0$, instantaneous selling is always optimal, which is consistent with the observations of \cite{DaiJinZhoZho10} or \cite{ShiXuZho08} for the Black-Scholes model in finite horizon. On the contrary, for a relative quadratic error criterion, $f:y \mapsto {(1-y)^2}$, selling is optimal as soon as the process $X$ crosses a specified function $\varphi$ of its running maximum $X^*$. These results reinforce the idea that optimal stopping problems of similar type lead easily to selling rules of very different nature. Nevertheless, our numerical experiments suggest that the practical optimal selling rule for the relative quadratic error criterion is in fact very close to immediate selling.
dc.relation.isversionofjnlnameMathematical Finance
dc.relation.isversionofjnlvol25
dc.relation.isversionofjnlissue4
dc.relation.isversionofjnldate2015
dc.relation.isversionofjnlpages754-788
dc.relation.isversionofdoihttp://dx.doi.org/10.1111/mafi.12036
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-00573429
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherBlackwell
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingprintoui
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dc.description.halcandidateoui
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2016-11-29T15:45:58Z


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