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

X. Mao, J. Appleby, T. Lynch, H. Wu

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1 Citation (Scopus)
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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.
Original languageEnglish
Pages (from-to)135-166
Number of pages31
JournalCommunications in Applied Analysis
Volume13
Issue number2
Publication statusPublished - 19 Jan 2009

Keywords

  • fluctuations
  • stochastic
  • Markovian switching
  • logarithm
  • market

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