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

Monoyios, Michael (2005) The minimal entropy measure and an Esscher transform in an incomplete market model. . . (Submitted)

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Abstract

We consider an incomplete market model with one traded stock and two correlated Brownian motions $W$ , $\widetilde{W}$ . The Brownian motion $W$ drives the stock price, whose volatility and Sharpe ratio are adapted to the filtration $\mathbb{F} := (\widetilde{\mathcal{F}}_{t})_{0 \le t \le T}$ generated by $\widetilde{W}$ . We show that the projections of the minimal entropy and minimal martingale measures onto $\widetilde{\mathcal{F}}_{T}$ are related by an Esscher transform involving the correlation between $W$ , $\widetilde{W}$ , and the mean-variance trade-off process. The result leads to a new formula for the marginal exponential utility-based price of an $\widetilde{\mathcal{F}}_{T}$ -measurable European claim.

Item Type:	Article
Subjects:	O - Z > Probability theory and stochastic processes
Research Groups:	Mathematical and Computational Finance Group
ID Code:	217
Deposited By:	Michael Monoyios
Deposited On:	11 Jan 2006
Last Modified:	20 Jul 2009 14:19

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The minimal entropy measure and an Esscher transform in an incomplete market model. (deposited 11 Jan 2006) [Currently Displayed]
- The minimal entropy measure and an Esscher transform in an incomplete market model. (deposited 06 Jul 2007)

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