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

Jean-Luc Prigent

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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.

Date: 1999-12
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Citations: View citations in EconPapers (5)

Published in Advances in Applied Probability, 1999, 31 (4), pp.1058-1077. ⟨10.1239/aap/1029955260⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03679524

DOI: 10.1239/aap/1029955260

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