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A model of financial market with several interacting assets. Complete market case

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  • Victoria Steblovskaya

    ()
    (Institut für Angewandte Mathematik, Universität Bonn, Wegelerstrasse, 6, D-53115 Bonn, Germany, SFB 256; BiBoS IZKS)

  • Sergio Albeverio

    ()
    (Institut für Angewandte Mathematik, Universität Bonn, Wegelerstrasse, 6, D-53115 Bonn, Germany, SFB 256; BiBoS IZKS)

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    Abstract

    A new model of a financial market is introduced extending the multidimensional Black-Scholes model to the case where several assets can interact with each other even in the absence of noise. Sufficient conditions for the existence of the equivalent martingale measure, absence of arbitrage and completeness are given. In the case of a complete market the pricing of contingent claims based on several assets (e.g. index options) is considered and explicit formulas are derived.

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    Bibliographic Info

    Article provided by Springer in its journal Finance and Stochastics.

    Volume (Year): 6 (2002)
    Issue (Month): 3 ()
    Pages: 383-396

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    Handle: RePEc:spr:finsto:v:6:y:2002:i:3:p:383-396

    Note: received: July 2000; final version received: October 2001
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    Related research

    Keywords: Multidimensional Black-Scholes model; linear stochastic differential equations with multiplicative noise; complete market; pricing of contingent claims;

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