Exponential Hedging and Entropic Penalties | Zendy

Delbaen Freddy | Zendy; Grandits Peter | Zendy; Rheinländer Thorsten | Zendy; Samperi Dominick | Zendy; Schweizer Martin | Zendy; Stricker Christophe | Zendy

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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.

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