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Exponential utility indifference valuation in two Brownian settings with stochastic correlation

  • Christoph Frei (a1) and Martin Schweizer (a1)
Abstract

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 V B 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 V B enjoys a monotonicity property in the correlation between tradable and nontradable assets.

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Copyright
Corresponding author
Postal address: Department of Mathematics, ETH Zürich, 8092 Zürich, Switzerland.
∗∗ Email address: christoph.frei@math.ethz.ch
∗∗∗ Email address: martin.schweizer@math.ethz.ch
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Advances in Applied Probability
  • ISSN: 0001-8678
  • EISSN: 1475-6064
  • URL: /core/journals/advances-in-applied-probability
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