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Sample quantiles of additive renewal reward processes

Part of: Markov processes Special processes

Published online by Cambridge University Press:  14 July 2016

Angelos Dassios
Angelos Dassios*
Affiliation:
London School of Economics
*
∗Postal address: Department of Statistics, London School of Economics, Houghton Street, London WC2A 2AE, UK.
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Abstract

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.

Keywords

SAMPLE QUANTILESLOOK-BACK FINANCIAL OPTIONSMARKED RENEWAL PROCESSES

MSC classification

Primary: 60K15: Markov renewal processes, semi-Markov processes 60J75: Jump processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 4 , December 1996 , pp. 1018 - 1032
Copyright
Copyright © Applied Probability Trust 1996 

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