Relationships between the stochastic discount factor and the optimal omega ratio

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dc.contributor.author Balbás, Alejandro
dc.contributor.author Balbás, Beatriz
dc.contributor.author Balbás, Raquel
dc.contributor.editor Universidad Carlos III de Madrid. Instituto para el Desarrollo Empresarial
dc.date.accessioned 2018-02-27T15:22:53Z
dc.date.available 2018-02-27T15:22:53Z
dc.date.issued 2018-02-01
dc.identifier.issn 1989-8843
dc.identifier.uri http://hdl.handle.net/10016/26348
dc.description.abstract The omega ratio is an interesting performance measure because it fo- cuses on both downside losses and upside gains, and nancial markets are re ecting more and more asymmetry and heavy tails. This paper focuses on the omega ratio optimization in general Banach spaces, which applies for both in nite dimensional approaches related to continuous time stochastic pricing models (Black and Scholes, stochastic volatility, etc.) and more classical problems in portfolio selection. New algorithms will be provided, as well as Fritz John-like and Karush-Kuhn-Tucker-like optimality conditions and duality results, despite the fact that omega is neither di¤er- entiable nor convex. The optimality conditions will be applied to the most important pricing models of Financial Mathematics, and it will be shown that the optimal value of omega only depends on the upper and lower bounds of the pricing model stochastic discount factor. In particular, if the stochastic discount factor is unbounded (Black and Scholes, Heston, etc.) then the optimal omega ratio becomes unbounded too (it may tend to in nity), and the introduction of several nancial constraints does not overcome this caveat. The new algorithms and optimality conditions will also apply to optimize omega in static frameworks, and it will be illustrated that both in nite- and nite-dimensional approaches may be useful to this purpose.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.relation.ispartofseries Working paper. Business Economic Series
dc.relation.ispartofseries 18-01
dc.rights Atribución-NoComercial-SinDerivadas 3.0 España
dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject.other Omega Ratio
dc.subject.other Asset Pricing Model
dc.subject.other Stochastic Discount Factor
dc.subject.other Representation Theorem
dc.subject.other Optimality Conditions
dc.title Relationships between the stochastic discount factor and the optimal omega ratio
dc.type workingPaper
dc.subject.jel G11
dc.subject.jel G12
dc.subject.jel C61
dc.subject.jel C65
dc.rights.accessRights openAccess
dc.type.version draft
dc.identifier.uxxi DT/0000001606
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