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Exponential Hedging and Entropic Penalties
Author(s) -
Delbaen Freddy,
Grandits Peter,
Rheinländer Thorsten,
Samperi Dominick,
Schweizer Martin,
Stricker Christophe
Publication year - 2002
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/1467-9965.02001
Subject(s) - semimartingale , martingale (probability theory) , mathematics , local martingale , exponential utility , martingale pricing , mathematical economics , bounded function , exponential function , probability measure , term (time) , expected utility hypothesis , mathematical finance , economics , discrete mathematics , financial economics , mathematical analysis , physics , quantum mechanics
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.