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

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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https://hal-cyu.archives-ouvertes.fr/hal-03679524
Contributor : Jean-Luc Prigent Connect in order to contact the contributor
Submitted on : Thursday, May 26, 2022 - 5:19:13 PM
Last modification on : Friday, August 5, 2022 - 2:46:00 PM

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Jean-Luc Prigent. Incomplete markets: convergence of options values under the minimal martingale measure. Advances in Applied Probability, 1999, 31 (4), pp.1058-1077. ⟨10.1239/aap/1029955260⟩. ⟨hal-03679524⟩

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