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Incomplete Markets: Convergence of Options Values under the Minimal Martingale Measure

Jean-Luc Prigent
Advances in Applied Probability
Vol. 31, No. 4 (Dec., 1999), pp. 1058-1077
Stable URL: http://www.jstor.org/stable/1428344
Page Count: 20
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Incomplete Markets: Convergence of Options Values under the Minimal Martingale Measure
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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.

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