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Exponential Hedging and Entropic Penalties

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

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.

Suggested Citation

  • Freddy Delbaen & Peter Grandits & Thorsten Rheinländer & Dominick Samperi & Martin Schweizer & Christophe Stricker, 2002. "Exponential Hedging and Entropic Penalties," Mathematical Finance, Wiley Blackwell, vol. 12(2), pages 99-123, April.
    • Handle: RePEc:bla:mathfi:v:12:y:2002:i:2:p:99-123
    DOI: 10.1111/1467-9965.02001
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