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Exponential utility indifference valuation in two Brownian settings with stochastic correlation

Part of: Stochastic systems and control Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Christoph Frei  and
Martin Schweizer
Christoph Frei*
Affiliation:
ETH Zürich
Martin Schweizer*
Affiliation:
ETH Zürich
*
∗ Postal address: Department of Mathematics, ETH Zürich, 8092 Zürich, Switzerland.
∗ Postal address: Department of Mathematics, ETH Zürich, 8092 Zürich, Switzerland.
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Abstract

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We study the exponential utility indifference valuation of a contingent claim B in an incomplete market driven by two Brownian motions. The claim depends on a nontradable asset stochastically correlated with the traded asset available for hedging. We use martingale arguments to provide upper and lower bounds, in terms of bounds on the correlation, for the value VB of the exponential utility maximization problem with the claim B as random endowment. This yields an explicit formula for the indifference value b of B at any time, even with a fairly general stochastic correlation. Earlier results with constant correlation are recovered and extended. The reason why all this works is that, after a transformation to the minimal martingale measure, the value VB enjoys a monotonicity property in the correlation between tradable and nontradable assets.

Keywords

Exponential utilityindifference valuationnontradable assetstochastic volatilityrandom endowmentdistortion powercorrelated Brownian motion

MSC classification

Secondary: 60G35: Signal detection and filtering 93E20: Optimal stochastic control
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 40 , Issue 2 , June 2008 , pp. 401 - 423
Copyright
Copyright © Applied Probability Trust 2008 

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