On the super replication price of unbounded claims

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dc.creatorBiagini, Sara
dc.creatorFrittelli, Marco
dc.date2005-03-24
dc.date.accessioned2026-07-07T12:07:15Z
dc.date.available2026-07-07T12:07:15Z
dc.descriptionIn an incomplete market the price of a claim f in general cannot be uniquely identified by no arbitrage arguments. However, the ``classical'' super replication price is a sensible indicator of the (maximum selling) value of the claim. When f satisfies certain pointwise conditions (e.g., f is bounded from below), the super replication price is equal to sup_QE_Q[f], where Q varies on the whole set of pricing measures. Unfortunately, this price is often too high: a typical situation is here discussed in the examples. We thus define the less expensive weak super replication price and we relax the requirements on f by asking just for ``enough'' integrability conditions. By building up a proper duality theory, we show its economic meaning and its relation with the investor's preferences. Indeed, it turns out that the weak super replication price of f coincides with sup_{Q\in M_Φ}E_Q[f], where M_Φ is the class of pricing measures with finite generalized entropy (i.e., E[Φ(\frac{dQ}{dP})]<\infty) and where Φis the convex conjugate of the utility function of the investor.
dc.descriptionPublished at http://dx.doi.org/10.1214/105051604000000459 in 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/0503550
dc.identifierhttp://arxiv.org/abs/math/0503550
dc.identifierAnnals of Applied Probability 2004, Vol. 14, No. 4, 1970-1991
dc.identifierdoi:10.1214/105051604000000459
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/208905
dc.subjectProbability
dc.subjectPricing of Securities
dc.subject60G42, 60G44 (Primary)
dc.titleOn the super replication price of unbounded claims
dc.typetext

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