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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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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creator Delbaen, Freddy
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description 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.
doi_str_mv 10.1111/1467-9965.02001
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source EconLit s plnými texty; International Bibliography of the Social Sciences (IBSS); Business Source Ultimate; Wiley
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
title Exponential Hedging and Entropic Penalties
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