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Incomplete markets: convergence of options values under the minimal martingale measure
Published online by Cambridge University Press: 01 July 2016
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.
MSC classification
- Type
- General Applied Probability
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- Copyright © Applied Probability Trust 1999
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