The Mathematical Institute, University of Oxford, Eprints Archive

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

Monoyios, Michael (2007) The minimal entropy measure and an Esscher transform in an incomplete market model. Statistics and Probability Letters, 77 . pp. 1070-1076.

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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:623
Deposited By:Michael Monoyios
Deposited On:06 Jul 2007
Last Modified:20 Jul 2009 14:22

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