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Finite Time Merton Strategy under Drawdown Constraint: A Viscosity Solution Approach

dc.contributor.authorElie, Romuald
dc.date.accessioned2009-07-02T12:30:45Z
dc.date.available2009-07-02T12:30:45Z
dc.date.issued2008
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/671
dc.language.isoenen
dc.subjectConsumption-investment strategy - Drawdown constraint - Viscosity solution - Comparison principleen
dc.subject.ddc519en
dc.titleFinite Time Merton Strategy under Drawdown Constraint: A Viscosity Solution Approachen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe consider the optimal consumption-investment problem under the drawdown constraint, i.e. the wealth process never falls below a fixed fraction of its running maximum. We assume that the risky asset is driven by the constant coefficients Black and Scholes model and we consider a general class of utility functions. On an infinite time horizon, Elie and Touzi (Preprint, [2006]) provided the value function as well as the optimal consumption and investment strategy in explicit form. In a more realistic setting, we consider here an agent optimizing its consumption-investment strategy on a finite time horizon. The value function interprets as the unique discontinuous viscosity solution of its corresponding Hamilton-Jacobi-Bellman equation. This leads to a numerical approximation of the value function and allows for a comparison with the explicit solution in infinite horizon.en
dc.relation.isversionofjnlnameApplied Mathematics and Optimization
dc.relation.isversionofjnlvol58en
dc.relation.isversionofjnlissue3en
dc.relation.isversionofjnldate2008-12
dc.relation.isversionofjnlpages411-431en
dc.relation.isversionofdoihttp://dx.doi.org/10.1007/s00245-008-9044-yen
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00362305/en/en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherSpringeren
dc.subject.ddclabelProbabilités et mathématiques appliquéesen


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