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A minimality property of the minimal martingale measure


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  • Schweizer, Martin
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    Let X be a continuous adapted process for which there exists an equivalent local martingale measure (ELMM). The minimal martingale measure is the unique ELMM for X with the property that local P-martingales strongly orthogonal to the P-martingale part of X are also local -martingales. We prove that if exists, it minimizes the reverse relative entropy H(PQ) over all ELMMs Q for X. A counterexample shows that the assumption of continuity cannot be dropped.

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    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 42 (1999)
    Issue (Month): 1 (March)
    Pages: 27-31

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    Handle: RePEc:eee:stapro:v:42:y:1999:i:1:p:27-31

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    Keywords: Minimal martingale measure Relative entropy Equivalent martingale measures;


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    1. N. Hofmann & E. Platen & M. Schweizer, 1992. "Option Pricing under Incompleteness and Stochastic Volatility," Discussion Paper Serie B 209, University of Bonn, Germany.
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    Cited by:
    1. Vicky Henderson, 2002. "Analytical Comparisons of Option prices in Stochastic Volatility Models," OFRC Working Papers Series, Oxford Financial Research Centre 2002mf03, Oxford Financial Research Centre.
    2. Basak, Suleyman & Chabakauri, Georgy, 2009. "Dynamic Mean-Variance Asset Allocation," CEPR Discussion Papers, C.E.P.R. Discussion Papers 7256, C.E.P.R. Discussion Papers.
    3. Vicky Henderson & David Hobson & Sam Howison & Tino Kluge, 2005. "A Comparison of Option Prices Under Different Pricing Measures in a Stochastic Volatility Model with Correlation," Review of Derivatives Research, Springer, Springer, vol. 8(1), pages 5-25, June.
    4. Monoyios, Michael, 2007. "The minimal entropy measure and an Esscher transform in an incomplete market model," Statistics & Probability Letters, Elsevier, Elsevier, vol. 77(11), pages 1070-1076, June.
    5. Gatfaoui Hayette & Chauveau Thierry, 2004. "Pricing and Hedging Options in Incomplete Markets: Idiosyncratic Risk, Systematic Risk and Stochastic Volatility," Finance, EconWPA 0404002, EconWPA.
    6. Hubalek, Friedrich & Sgarra, Carlo, 2009. "On the Esscher transforms and other equivalent martingale measures for Barndorff-Nielsen and Shephard stochastic volatility models with jumps," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 119(7), pages 2137-2157, July.
    7. Friedrich Hubalek & Carlo Sgarra, 2008. "On the Esscher transforms and other equivalent martingale measures for Barndorff-Nielsen and Shephard stochastic volatility models with jumps," Papers 0807.1227,
    8. Vicky Henderson & David Hobson & Sam Howison & Tino Kluge, 2003. "A Comparison of q-optimal Option Prices in a Stochastic Volatility Model with Correlation," OFRC Working Papers Series, Oxford Financial Research Centre 2003mf02, Oxford Financial Research Centre.
    9. Ioannis Karatzas & Constantinos Kardaras, 2007. "The numéraire portfolio in semimartingale financial models," Finance and Stochastics, Springer, vol. 11(4), pages 447-493, October.
    10. Stefan Kassberger & Thomas Liebmann, 2011. "Minimal q-entropy martingale measures for exponential time-changed Lévy processes," Finance and Stochastics, Springer, vol. 15(1), pages 117-140, January.


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