1-4 September 2015
Angers - France
Europe/Paris timezone

On the Chaotic Representation Property of Certain Families of Martingales

2 Sep 2015, 09:50
40m
Angers - France

Angers - France

Speaker

Hans-Jürgen Engelbert (Friedrich Schiller-University of Jena)

Description

In this talk, we shall discuss the chaotic representation property for certain families of square integrable martingales. Our approach extends well-known results on the Brownian motion or the compensated Poisson process in which case the family would only consist of a single martingale. The starting point for these investigations has been the problem of finding appropriate families of martingales related to Lévy processes satisfying the chaotic (or only predictable) representation property. In particular, we extend the results of Nualart and Schoutens on the chaotic representation property of the Teugels martingales. In the context of Mathematical Finance, families of martingales enjoying the chaotic (and hence predictable) representation property can serve for the completion of an (incomplete) financial market. As a linear or geometric Lévy market is normally incomplete, our approach can be applied to construct different completions of the market, in the sense that there will be added to the stock and the bank account a certain family of contingent claims, the terminal values of the martingales from the family under consideration.

Primary author

Hans-Jürgen Engelbert (Friedrich Schiller-University of Jena)

Presentation Materials