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Asymptotic analysis of forward performance processes in incomplete markets and their ill-posed HJB equations

Author(s): Shkolnikov, Mykhaylo; Sircar, Ronnie; Zariphopoulou, Thaleia

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dc.contributor.authorShkolnikov, Mykhaylo-
dc.contributor.authorSircar, Ronnie-
dc.contributor.authorZariphopoulou, Thaleia-
dc.date.accessioned2021-10-11T14:17:54Z-
dc.date.available2021-10-11T14:17:54Z-
dc.date.issued2016en_US
dc.identifier.citationShkolnikov, Mykhaylo, Sircar, Ronnie, Zariphopoulou, Thaleia. (Asymptotic analysis of forward performance processes in incomplete markets and their ill-posed HJB equationsen_US
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/pr1k57c-
dc.description.abstractWe consider the problem of optimal portfolio selection under forward investment performance criteria in an incomplete market. The dynamics of the prices of the traded assets depend on a pair of stochastic factors, namely, a slow factor (e.g. a macroeconomic indicator) and a fast factor (e.g. stochastic volatility). We analyze the associated forward performance SPDE and provide explicit formulae for the leading order and first order correction terms for the forward investment process and the optimal feedback portfolios. They both depend on the investor's initial preferences and the dynamically changing investment opportunities. The leading order terms resemble their time-monotone counterparts, but with the appropriate stochastic time changes resulting from averaging phenomena. The first-order terms compile the reaction of the investor to both the changes in the market input and his recent performance. Our analysis is based on an expansion of the underlying ill-posed HJB equation, and it is justified by means of an appropriate remainder estimate.en_US
dc.language.isoen_USen_US
dc.relation.ispartofSIAM Journal on Financial Mathematicsen_US
dc.rightsAuthor's manuscripten_US
dc.titleAsymptotic analysis of forward performance processes in incomplete markets and their ill-posed HJB equationsen_US
dc.typeJournal Articleen_US
pu.type.symplectichttp://www.symplectic.co.uk/publications/atom-terms/1.0/journal-articleen_US

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