The minimal entropy measure and an Esscher transform in an incomplete market model
AbstractWe 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 InfoArticle provided by Elsevier in its journal Statistics & Probability Letters.
Volume (Year): 77 (2007)
Issue (Month): 11 (June)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
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- 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.
- Schweizer, Martin, 1999. "A minimality property of the minimal martingale measure," Statistics & Probability Letters, Elsevier, vol. 42(1), pages 27-31, March.
- Thaleia Zariphopoulou, 2001. "A solution approach to valuation with unhedgeable risks," Finance and Stochastics, Springer, vol. 5(1), pages 61-82.
- 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.
- Scott Robertson, 2012. "Pricing for Large Positions in Contingent Claims," Papers 1202.4007, arXiv.org, revised Dec 2013.
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