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

Author

Listed:
  • Thomas Goll

    (Institut für Mathematische Stochastik, Universität Freiburg i. Br., Eckerstraße 1, 79104 Freiburg i. Br., Germany Manuscript)

  • Ludger Rüschendorf

    (Institut für Mathematische Stochastik, Universität Freiburg i. Br., Eckerstraße 1, 79104 Freiburg i. Br., Germany Manuscript)

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.

Suggested Citation

  • Thomas Goll & Ludger Rüschendorf, 2001. "Minimax and minimal distance martingale measures and their relationship to portfolio optimization," Finance and Stochastics, Springer, vol. 5(4), pages 557-581.
    • Handle: RePEc:spr:finsto:v:5:y:2001:i:4:p:557-581
    Note: received: January 2000; final version received: February 2001
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    More about this item

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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