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Incomplete markets: convergence of options values under the minimal martingale measure

Part of: Stochastic processes Limit theorems

Published online by Cambridge University Press:  01 July 2016

Jean-Luc Prigent
Jean-Luc Prigent*
Affiliation:
University of Cergy-Pontoise
*
∗ Postal address: Thema, University of Cergy-Pontoise, 33 Bd du Port, 95000 Cergy, France. Email address: prigent@u_cergy.fr
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Abstract

In the setting of incomplete markets, this paper presents a general result of convergence for derivative assets prices. It is proved that the minimal martingale measure first introduced by Föllmer and Schweizer is a convenient tool for the stability under convergence. This extends previous well-known results when the markets are complete both in discrete time and continuous time. Taking into account the structure of stock prices, a mild assumption is made. It implies the joint convergence of the sequences of stock prices and of the Radon-Nikodym derivative of the minimal measure. The convergence of the derivatives prices follows.

This property is illustrated in the main classes of financial market models.

Keywords

Weak convergenceminimal martingale measureincomplete financial markets

MSC classification

Primary: 60F05: Central limit and other weak theorems 60G35: Signal detection and filtering
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 31 , Issue 4 , December 1999 , pp. 1058 - 1077
Copyright
Copyright © Applied Probability Trust 1999 

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