This is an announcement for the paper "Utility-based super-replication prices of unbounded contingent claims and duality of cones" by Frank Oertel and Mark Owen.
Abstract: Consider a financial market in which an agent trades with utility-induced restrictions on wealth. We prove that the utility-based super-replication price of an unbounded (but sufficiently integrable) contingent claim is equal to the supremum of its discounted expectations under pricing measures with finite entropy. Central to our proof is the representation of a cone $C_\V$ of utility-based super-replicable contingent claims as the polar cone of the set of finite entropy separating measures. $C_\V$ is shown to be the closure, under a relevant weak topology, of the cone of all (sufficiently integrable) contingent claims that can be dominated by a zero-financed terminal wealth. As our approach shows, those terminal wealths need {\it not} necessarily stem from {\it admissible} trading strategies only. We investigate also the natural dual of this result, and show that the polar cone of $C_\V$ is the cone generated by separating measures with {\it finite loss-entropy}. For an agent whose utility function is unbounded from above, the set of pricing measures with finite loss-entropy can be slightly larger than the set of pricing measures with finite entropy. Indeed, we prove that the former set is the closure of the latter under a suitable weak topology. Finally, we show how our framework can be applied to another field of mathematical economics and how it sheds a different light on Farkas' Lemma and its infinite dimensional version there.
Archive classification: Probability; Functional Analysis; Optimization and Control
Mathematics Subject Classification: 1B16, 46N10, 60G44
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Submitted from: f.oertel@ucc.ie
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