Exponential Hedging and Entropic Penalties

We solve the problem of hedging a contingent claim B by maximizing the expected exponential utility of terminal net wealth for a locally bounded semimartingale X. We prove a duality relation between this problem and a dual problem for local martingale measures Q for X where we either minimize relati...

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Bibliographic Details
Published in:Mathematical finance 2002-04, Vol.12 (2), p.99-123
Main Authors: Delbaen, Freddy, Grandits, Peter, Rheinländer, Thorsten, Samperi, Dominick, Schweizer, Martin, Stricker, Christophe
Format: Article
Language:English
Subjects:
duality
Entropy
exponential utility
Hedging
Investment
Mathematical models
minimal entropy martingale measure
minimal martingale measure
relative entropy
reverse Hölder inequalities
Risk
Studies
Utility functions
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Summary:We solve the problem of hedging a contingent claim B by maximizing the expected exponential utility of terminal net wealth for a locally bounded semimartingale X. We prove a duality relation between this problem and a dual problem for local martingale measures Q for X where we either minimize relative entropy minus a correction term involving B or maximize the Q‐price of B subject to an entropic penalty term. Our result is robust in the sense that it holds for several choices of the space of hedging strategies. Applications include a new characterization of the minimal martingale measure and risk‐averse asymptotics.
ISSN:0960-1627
1467-9965
DOI:10.1111/1467-9965.02001