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Article Dans Une Revue Advances in Applied Probability Année : 1999

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

Résumé

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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Dates et versions

hal-03679524 , version 1 (26-05-2022)

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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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