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

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  • Monoyios, Michael

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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  • Monoyios, Michael, 2007. "The minimal entropy measure and an Esscher transform in an incomplete market model," Statistics & Probability Letters, Elsevier, vol. 77(11), pages 1070-1076, June.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:11:p:1070-1076
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    References listed on IDEAS

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    1. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(2), pages 427-429, April.
    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. David Hobson, 2004. "STOCHASTIC VOLATILITY MODELS, CORRELATION, AND THE q‐OPTIMAL MEASURE," Mathematical Finance, Wiley Blackwell, vol. 14(4), pages 537-556, October.
    4. Thaleia Zariphopoulou, 2001. "A solution approach to valuation with unhedgeable risks," Finance and Stochastics, Springer, vol. 5(1), pages 61-82.
    5. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(1), pages 223-229, February.
    6. 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.
    7. Schweizer, Martin, 1999. "A minimality property of the minimal martingale measure," Statistics & Probability Letters, Elsevier, vol. 42(1), pages 27-31, March.
    8. 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.
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    Cited by:

    1. Weidong Tian & Daisuke Yoshikawa, 2017. "Analyzing Equilibrium in Incomplete Markets with Model Uncertainty," International Review of Finance, International Review of Finance Ltd., vol. 17(2), pages 235-262, June.
    2. Matthias R. Fengler & Helmut Herwartz & Christian Werner, 2012. "A Dynamic Copula Approach to Recovering the Index Implied Volatility Skew," Journal of Financial Econometrics, Oxford University Press, vol. 10(3), pages 457-493, June.
    3. Tahir Choulli & Ella Elazkany & Mich`ele Vanmaele, 2024. "The second-order Esscher martingale densities for continuous-time market models," Papers 2407.03960, arXiv.org.
    4. Scott Robertson, 2012. "Pricing for Large Positions in Contingent Claims," Papers 1202.4007, arXiv.org, revised Dec 2013.
    5. Thorsten Rheinländer & Jenny Sexton, 2011. "Hedging Derivatives," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8062, September.

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