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On Comparison Theorem and its Applications to Finance

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Optimality and Risk - Modern Trends in Mathematical Finance

Abstract

This paper studies a comparison theorem for solutions of stochastic differential equations and its generalization to the multi-dimensional case. We show, that even though the proof of the generalized theorem follows that of the one-dimensional comparison theorem, the multi-dimensional case requires a different condition on the drift coefficient, known in the theory of differential equations as Kamke-Wazewski condition. We also present several examples of possible applications to option price estimation in finance.

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Authors and Affiliations

  1. Department of Mathematical and Statistical Sciences, University of Alberta, 632 Central Academic Building, Edmonton, AB, T6G 2G1, Canada

    Vladislav Y. Krasin & Alexander V. Melnikov

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  1. Vladislav Y. Krasin
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  2. Alexander V. Melnikov
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Correspondence to Alexander V. Melnikov .

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Krasin, V.Y., Melnikov, A.V. (2009). On Comparison Theorem and its Applications to Finance. In: Optimality and Risk - Modern Trends in Mathematical Finance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02608-9_8

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