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The size of the largest fluctuations in a market model with Markovian switching

Mao, X. and Appleby, J. and Lynch, T. and Wu, H. (2009) The size of the largest fluctuations in a market model with Markovian switching. Communications in Applied Analysis, 13 (2). pp. 135-166. ISSN 1083-2564

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    Abstract

    This paper considers the size of the large fluctuations of a stochastic differential equation with Markovian switching. We concentrate on processes which obey the Law of the Iterated Logarithm, or obey upper and lower iterated logarithm growth bounds on their almost sure partial maxima. The results are applied to financial market models which are subject to random regime shifts. We prove that the security exhibits the same long-run growth properties and deviations from the trend rate of growth as conventional geometric Brownian motion, and also that the returns, which are non-Gaussian, still exhibit the same growth rate in their almost sure large deviations as stationary continuous-time Gaussian processes.

    Item type: Article
    ID code: 13997
    Keywords: fluctuations, stochastic, Markovian switching, logarithm, market, Mathematics, Modelling and Simulation, Analysis, Applied Mathematics, Numerical Analysis
    Subjects: Science > Mathematics
    Department: Faculty of Science > Mathematics and Statistics
    Related URLs:
      Depositing user: Mrs Carolynne Westwood
      Date Deposited: 16 Dec 2009 09:56
      Last modified: 04 Sep 2014 23:46
      URI: http://strathprints.strath.ac.uk/id/eprint/13997

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