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2 results

  • Last Exit Before an Exponential Time for Spectrally Negative Lévy Processes

  • Part of
  • E. J. Baurdoux
  • Journal:
    Journal of Applied Probability / Volume 46 / Issue 2 / June 2009
    Published online by Cambridge University Press:
    14 July 2016, pp. 542-558
    Print publication:
    June 2009
    • Article
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  • Chiu and Yin (2005) found the Laplace transform of the last time a spectrally negative Lévy process, which drifts to ∞, is below some level. The main motivation for the study of this random time stems from risk theory: what is the last time the risk process, modeled by a spectrally negative Lévy process drifting to ∞, is 0? In this paper we extend the result of Chiu and Yin, and we derive the Laplace transform of the last time, before an independent, exponentially distributed time, that a spectrally negative Lévy process (without any further conditions) exceeds (upwards or downwards) or hits a certain level. As an application, we extend a result found in Doney (1991).

  • Last passage times of minimum contrast estimators

  • Part of
  • Arup Bose, Snigdhansu Chatterjee
  • Journal:
    Journal of the Australian Mathematical Society / Volume 71 / Issue 1 / August 2001
    Published online by Cambridge University Press:
    09 April 2009, pp. 1-10
    Print publication:
    August 2001
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  • We study the last passage time and its asymptotic distribution for minimum contrast estimators defined through the minimization of a convex criterion function based on U-functionals. This includes cases of non-smooth estimators for vector valued parameters. We also derive a Bahadur-type representation and the law of iterated logarithms for such estimators.