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An entropy approach to the Stein and Stein model with correlation

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  • Thorsten Rheinländer

Abstract

We outline a martingale duality method for determining the minimal entropy martingale measure in a general continuous semimartingale model, and provide the relevant verification results. This method is illustrated by a detailed case study of the Stein and Stein stochastic volatility model driven by two correlated Brownian motions. It turns out that in case the mean reversion level and the correlation coefficient are nonzero, an investor who can use trading strategies adapted to the Brownian filtration may achieve a higher expected exponential utility from terminal wealth than an investor who can only observe the price process. Copyright Springer-Verlag Berlin/Heidelberg 2005

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  • Thorsten Rheinländer, 2005. "An entropy approach to the Stein and Stein model with correlation," Finance and Stochastics, Springer, vol. 9(3), pages 399-413, July.
    • Handle: RePEc:spr:finsto:v:9:y:2005:i:3:p:399-413
    DOI: 10.1007/s00780-004-0149-0
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    References listed on IDEAS

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    1. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," The Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-752.
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    3. David Heath & Eckhard Platen & Martin Schweizer, 2001. "A Comparison of Two Quadratic Approaches to Hedging in Incomplete Markets," Mathematical Finance, Wiley Blackwell, vol. 11(4), pages 385-413, October.
    4. 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.
    5. Marco Frittelli, 2000. "The Minimal Entropy Martingale Measure and the Valuation Problem in Incomplete Markets," Mathematical Finance, Wiley Blackwell, vol. 10(1), pages 39-52, January.
    6. Jean-Paul Laurent & Huyen Pham, 1999. "Dynamic programming and mean-variance hedging," Post-Print hal-03675953, HAL.
    7. Francesca Biagini & Paolo Guasoni & Maurizio Pratelli, 2000. "Mean‐Variance Hedging for Stochastic Volatility Models," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 109-123, April.
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    Cited by:

    1. Thorsten Rheinländer & Gallus Steiger, 2010. "Utility Indifference Hedging with Exponential Additive Processes," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 17(2), pages 151-169, June.
    2. 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, arXiv.org.
    3. Smimou, K. & Bector, C.R. & Jacoby, G., 2007. "A subjective assessment of approximate probabilities with a portfolio application," Research in International Business and Finance, Elsevier, vol. 21(2), pages 134-160, June.
    4. Carole Bernard & Zhenyu Cui & Don McLeish, 2013. "On the martingale property in stochastic volatility models based on time-homogeneous diffusions," Papers 1310.0092, arXiv.org, revised Jul 2014.
    5. Thorsten Rheinländer & Jenny Sexton, 2011. "Hedging Derivatives," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8062, August.
    6. Paolo Guasoni & Scott Robertson, 2012. "Portfolios and risk premia for the long run," Papers 1203.1399, arXiv.org.

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