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

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

Research output: Contribution to journalArticle

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

Fingerprint

Markovian Switching
Market Model
Fluctuations
Law of the Iterated Logarithm
Financial Markets
Long-run
Gaussian Process
Large Deviations
Logarithm
Deviation
Partial
Motion
Trends
Financial markets

Keywords

  • fluctuations
  • stochastic
  • Markovian switching
  • logarithm
  • market

Cite this

Mao, X. ; Appleby, J. ; Lynch, T. ; Wu, H. / The size of the largest fluctuations in a market model with Markovian switching. In: Communications in Applied Analysis. 2009 ; Vol. 13, No. 2. pp. 135-166.
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The size of the largest fluctuations in a market model with Markovian switching. / Mao, X.; Appleby, J.; Lynch, T.; Wu, H.

In: Communications in Applied Analysis, Vol. 13, No. 2, 19.01.2009, p. 135-166.

Research output: Contribution to journalArticle

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