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 |
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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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