Completion of a Lévy market by power-jump assets
type: Item
instance of: scholarly article
title: Completion of a Lévy market by power-jump assets
zbMATH Open document ID: 1063.91021
author: David Nualart
author: Wim Schoutens
author: José Manuel Corcuera
published in: Finance and Stochastics
publication date: 2005-05-20T00:00:00Z
review text: The authors deal with the so-called (geometric) Lévy market model. Under this model the stock price process is modelled by a stochastic differential equation driven by a general Lévy process. Except for the geometric Brownian and the geometric Poissonian model, there are many equivalent martingale measures for the above-described general geometric Lévy market models, and such markets are incomplete: contingent claims cannot in general be hedged by a self-financing portfolio. The authors propose to enlarge the market by a series of very special assets related to the power-jump processes of the underlying Lévy process. A martingale representation theorem in terms of these (orthonormalized) power-jump processes leads to market completeness. In the second part it is assumed that the market is already enlarged by these so-called power-jump assets. The problem is whether the market is arbitrage free and complete. Existence of an equivalent martingale measure making not only a discounted stock price a martingale, but also all discounted prices of the newly introduced assets is studied. This problem is related to the moment problem.
reviewed by: Yuliya S. Mishura
Mathematics Subject Classification ID: 91B26
Mathematics Subject Classification ID: 91B16
Mathematics Subject Classification ID: 91B70
Mathematics Subject Classification ID: 91G80
Mathematics Subject Classification ID: 60H15
zbMATH DE Number: 2169556
zbMATH Keywords: market models
zbMATH Keywords: martingales
zbMATH Keywords: arbitrage
zbMATH Keywords: moment problem
zbMATH Keywords: orthogonal polynomials
MaRDI profile type: Publication
full work available at URL: s00780-004-0139-2
OpenAlex ID: W2033242254
DOI: 10.1007/S00780-004-0139-2
description: scientific article; zbMATH DE number 2169556