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Probability and Computational Finance Seminar
Scott Robertson
Carnegie Mellon University
Title: Utility Indifference Pricing in the Large Claim Limit

Abstract: We consider the problem of computing utility based prices for a contingent claim in the limit of a large position in the claim. The goal is to provide an alternative to the approximations for utility based prices in the case of a small number of claims. It is shown, in a general semi-martingale model, that the investor's absolute risk aversion near negative infinity is the sole determinant of the utility indifference price in that all investors with a given limiting risk aversion price like the same (exponential) investor. Based upon these results, it is natural to consider when an exponential investor, acting optimally, finds herself owning an over larger position in a contingent claim. In a general basis risk model, it is shown that the large claim limit arises precisely when a) the market is becoming complete, in that instantaneous correlations between the traded and non-traded asset are approaching one and b) the investor may purchase claims at a price different than the unique arbitrage free price in the limiting model.

Date: Monday, November 7, 2011
Time: 5:00 pm
Location: Wean Hall 6423
Submitted by:  Scott Robertson