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2 results

  • Sample quantiles of additive renewal reward processes

  • Part of
  • Angelos Dassios
  • Journal:
    Journal of Applied Probability / Volume 33 / Issue 4 / December 1996
    Published online by Cambridge University Press:
    14 July 2016, pp. 1018-1032
    Print publication:
    December 1996

  • The distribution of the sample quantiles of random processes is important for the pricing of some of the so-called financial ‘look-back' options. In this paper a representation of the distribution of the α-quantile of an additive renewal reward process is obtained as the sum of the supremum and the infimum of two rescaled independent copies of the process. This representation has already been proved for processes with stationary and independent increments. As an example, the distribution of the α-quantile of a randomly observed Brownian motion is obtained.