Exponential Hedging and Entropic Penalties

Freddy Delbaen, Peter Grandits, Thorsten Rheinländer, Dominick Samperi, Martin Schweizer and Christophe Stricker

Mathematical Finance, 2002, vol. 12, issue 2, 99-123

Abstract: 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.

Date: 2002
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