Philip Protter - Issues of Incomplete Markets

Seminar | October 16 | 3:30-5 p.m. | 3108 Etcheverry Hall

 Philip Protter, Columbia University

 Industrial Engineering & Operations Research

Abstract: In a complete market, there is a unique risk neutral measure, unique prices, and all contingent claims can be (at least theoretically) perfectly hedged. In an incomplete market, in contrast, there is an infinite number of risk neutral measures, a continuum of “fair” prices, and contingent claims can in general not be perfectly hedged, even theoretically. Unfortunately, there seems to be plenty of evidence markets in actuality are incomplete.

We are interested in trying to understand this a priori confusing situation. To make things concrete, we address the following question: Suppose a sequence of incomplete markets “converges” to a complete market in an appropriate sense (to be defined), do the major objects also converge? Mostly, this is false: the ranges of option prices do not converge, for example. We work out some simple examples that illustrate some of the issues, and we indicate when one might have some kind of reasonable convergence of the markets, and what such a convergence might be.

The talk is back on joint work with Jean Jacod.

Light refreshments will be served., 510-642-6222