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Probability and Computational Finance Seminar
Kim Weston
Carnegie Mellon University
Title: The Muckenhoupt (Ap) condition and the existence of an optimal martingale measure in optimal investment.

Abstract: An unpleasant qualitative feature of the general theory of optimal investment is that the dual optimizer may not correspond to the density of a martingale measure. The existence of such a dual optimal martingale measure is often desirable. For instance, in pricing theory, its existence is equivalent to the uniqueness of marginal utility based prices for all bounded contingent claims.

In this talk, I will show that the dual optimizer is the density of a martingale measure if one can find a $p>1$ such that

(i) There is a martingale measure whose density process satisfies the Muckenhoupt (Ap) condition from BMO spaces;

(ii) The relative risk-aversion of the utility function is bounded below by $1/q = 1-1/p$ and above by a constant.

In particular, condition (i) holds for the minimal martingale measure if the market price of risk is bounded. This is joint work with Dmitry Kramkov.

Date: Monday, March 16, 2015
Time: 4:30 pm
Location: Wean Hall 6423
Submitted by:  Dmitry Kramkov