Journal of Applied Probability

The Markov consistency of Archimedean survival processes

J. Jakubowski and A. Pytel

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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.

Article information

J. Appl. Probab., Volume 53, Number 2 (2016), 392-409.

First available in Project Euclid: 17 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J25: Continuous-time Markov processes on general state spaces
Secondary: 91G80: Financial applications of other theories (stochastic control, calculus of variations, PDE, SPDE, dynamical systems)

Gamma random bridge Markovian consistency Archimedean survival process profitability


Jakubowski, J.; Pytel, A. The Markov consistency of Archimedean survival processes. J. Appl. Probab. 53 (2016), no. 2, 392--409.

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