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Martingales and stochastic integrals in the theory of continuous trading

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  • Harrison, J. Michael
  • Pliska, Stanley R.
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    Abstract

    This paper develops a general stochastic model of a frictionless security market with continuous trading. The vector price process is given by a semimartingale of a certain class, and the general stochastic integral is used to represent capital gains. Within the framework of this model, we discuss the modern theory of contingent claim valuation, including the celebrated option pricing formula of Black and Scholes. It is shown that the security market is complete if and only if its vector price process has a certain martingale representation property. A multidimensional generalization of the Black-Scholes model is examined in some detail, and some other examples are discussed briefly.

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    File URL: http://www.sciencedirect.com/science/article/B6V1B-45FCS8R-X/2/704cb95b1dd0bed7e644304046fe4aab
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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 11 (1981)
    Issue (Month): 3 (August)
    Pages: 215-260

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    Handle: RePEc:eee:spapps:v:11:y:1981:i:3:p:215-260

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    Related research

    Keywords: Contingent claim valuation continous trading diffusion processes option pricing representation of martingales semimartingales stochastic integrals;

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