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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Victoria Steblovskaya & Sergio Albeverio, 2002. "A model of financial market with several interacting assets. Complete market case," Finance and Stochastics, Springer, vol. 6(3), pages 383-396.
  • 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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    Cited by:

    1. Albeverio, Sergio & Smii, Boubaker, 2015. "Asymptotic expansions for SDE’s with small multiplicative noise," Stochastic Processes and their Applications, Elsevier, vol. 125(3), pages 1009-1031.

    More about this item

    Keywords

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

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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