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The minimal entropy measure and an Esscher transform in an incomplete market model

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  • Monoyios, Michael
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    Abstract

    We consider an incomplete market model with one traded stock and two correlated Brownian motions . The Brownian motion W drives the stock price, whose volatility and Sharpe ratio are adapted to the filtration generated by . We show that the projections of the minimal entropy and minimal martingale measures onto are related by an Esscher transform involving the correlation between , and the mean-variance trade-off process. The result leads to a new formula for the marginal exponential utility-based price of an -measurable European claim.

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    Bibliographic Info

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

    Volume (Year): 77 (2007)
    Issue (Month): 11 (June)
    Pages: 1070-1076

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    Handle: RePEc:eee:stapro:v:77:y:2007:i:11:p:1070-1076

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    Related research

    Keywords: Minimal entropy measure Minimal martingale measure Esscher transform;

    References

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    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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    1. David Hobson, 2004. "STOCHASTIC VOLATILITY MODELS, CORRELATION, AND THE "q"-OPTIMAL MEASURE," Mathematical Finance, Wiley Blackwell, vol. 14(4), pages 537-556.
    2. Becherer, Dirk, 2003. "Rational hedging and valuation of integrated risks under constant absolute risk aversion," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 1-28, August.
    3. Thaleia Zariphopoulou, 2001. "A solution approach to valuation with unhedgeable risks," Finance and Stochastics, Springer, vol. 5(1), pages 61-82.
    4. Tehranchi, Michael, 2004. "Explicit solutions of some utility maximization problems in incomplete markets," Stochastic Processes and their Applications, Elsevier, vol. 114(1), pages 109-125, November.
    5. 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.
    6. Schweizer, Martin, 1999. "A minimality property of the minimal martingale measure," Statistics & Probability Letters, Elsevier, vol. 42(1), pages 27-31, March.
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    Cited by:
    1. Matthias R. Fengler & Helmut Herwartz & Christian Werner, 2012. "A Dynamic Copula Approach to Recovering the Index Implied Volatility Skew," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 10(3), pages 457-493, June.
    2. Scott Robertson, 2012. "Pricing for Large Positions in Contingent Claims," Papers 1202.4007, arXiv.org, revised Dec 2013.

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