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Stochastic Viability and Comparison Theorems for Mixed Stochastic Differential Equations

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Abstract

For a mixed stochastic differential equation containing both Wiener process and a Hölder continuous process with exponent γ > 1/2, we prove a stochastic viability theorem. As a consequence, we get a result about positivity of solution and a pathwise comparison theorem. An application to option price estimation is given.

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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

    Alexander Melnikov

  2. Faculty of Mechanics and Mathematics, Department of Probability, Statistics and Actuarial Mathematics, Kyiv National Taras Shevchenko University, Volodymyrska 64, 01601, Kyiv, Ukraine

    Yuliya Mishura & Georgiy Shevchenko

Authors
  1. Alexander Melnikov
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  2. Yuliya Mishura
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  3. Georgiy Shevchenko
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Correspondence to Georgiy Shevchenko.

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Melnikov, A., Mishura, Y. & Shevchenko, G. Stochastic Viability and Comparison Theorems for Mixed Stochastic Differential Equations. Methodol Comput Appl Probab 17, 169–188 (2015). https://doi.org/10.1007/s11009-013-9336-9

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  • DOI: https://doi.org/10.1007/s11009-013-9336-9

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