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Finance and Stochastics

, Volume 5, Issue 4, pp 557–581 | Cite as

Minimax and minimal distance martingale measures and their relationship to portfolio optimization

  • Thomas Goll
  • Ludger Rüschendorf

Abstract.

In this paper we give a characterization of minimal distance martingale measures with respect to f-divergence distances in a general semimartingale market model. We provide necessary and sufficient conditions for minimal distance martingale measures and determine them explicitly for exponential Lévy processes with respect to several classical distances. It is shown that the minimal distance martingale measures are equivalent to minimax martingale measures with respect to related utility functions and that optimal portfolios can be characterized by them. Related results in the context of continuous-time diffusion models were first obtained by He and Pearson (1991b) and Karatzas et al. (1991) and in a general semimartingale setting by Kramkov and Schachermayer (1999). Finally parts of the results are extended to utility-based hedging.

Key words:f-divergences, derivative pricing, utility maximization, hedging 
JEL Classification: G11, G13 
AMS (2000) Subject Classification: 62P05, 91B24, 91B28 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Thomas Goll
    • 1
  • Ludger Rüschendorf
    • 1
  1. 1.Institut für Mathematische Stochastik, Universität Freiburg i. Br., Eckerstraße 1, 79104 Freiburg i. Br., Germany (e-mail: goll@stochastik.uni-freiburg.de; ruschen@stochastik.uni-freiburg.de)DE

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