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The Markov consistency of Archimedean survival processes

Published online by Cambridge University Press:  21 June 2016

J. Jakubowski*
Affiliation:
University of Warsaw and Warsaw University of Technology
A. Pytel*
Affiliation:
Warsaw University of Technology
*
* Postal address: Faculty of Mathematics and Information Science, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warsaw, Poland.
* Postal address: Faculty of Mathematics and Information Science, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warsaw, Poland.

Abstract

In this paper we connect Archimedean survival processes (ASPs) with the theory of Markov copulas. ASPs were introduced by Hoyle and Mengütürk (2013) to model the realized variance of two assets. We present some new properties of ASPs related to their dependency structure. We study weak and strong Markovian consistency properties of ASPs. An ASP is weak Markovian consistent, but generally not strong Markovian consistent. Our results contain necessary and sufficient conditions for an ASP to be strong Markovian consistent. These properties are closely related to the concept of Markov copulas, which is very useful in modelling different dependence phenomena. At the end we present possible applications.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 2016 

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