The Mathematical Institute, University of Oxford, Eprints Archive

Utility indifference pricing with market incompleteness

Monoyios, Michael (2008) Utility indifference pricing with market incompleteness. In: Nonlinear Models in Mathematical Finance: New Research Trends in Option Pricing. Nova Science Publishers, Hauppage, New York, USA. ISBN 978 1 60456 931 5 (In Press)

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Abstract

Utility indifference pricing and hedging theory is presented, showing
how it leads to linear or to non-linear pricing rules for contingent
claims. Convex duality is first used to derive probabilistic
representations for exponential utility-based prices, in a general
setting with locally bounded semi-martingale price processes. The
indifference price for a finite number of claims gives a non-linear
pricing rule, which reduces to a linear pricing rule as the number of
claims tends to zero, resulting in the so-called marginal
utility-based price of the claim. Applications to basis risk models
with lognormal price processes, under full and partial information
scenarios are then worked out in detail. In the full information case,
a claim on a non-traded asset is priced and hedged using a correlated
traded asset. The resulting hedge requires knowledge of the drift
parameters of the asset price processes, which are very difficult to
estimate with any precision. This leads naturally to a further
application, a partial information problem, with the drift parameters
assumed to be random variables whose values are revealed to the hedger
in a Bayesian fashion via a filtering algorithm. The indifference
price is given by the solution to a non-linear PDE, reducing to a
linear PDE for the marginal price when the number of claims becomes
infinitesimally small.

Item Type:Book Section
Subjects:D - G > Game theory, mathematical finance, economics, social and behavioral sciences
O - Z > Probability theory and stochastic processes
Research Groups:Mathematical and Computational Finance Group
ID Code:724
Deposited By:Michael Monoyios
Deposited On:04 Aug 2008
Last Modified:20 Jul 2009 14:23

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