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Summary

The Archimedean Survival Process (ASP), which is quite interesting from a theoretical point of view, originates in some financial applications. It turns out that applications of ASP and ASP structures go beyond finance. ASPs are very interesting objects to study in the context of stochastic structures, both from the theoretical and applied perspective.

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.

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10 - Archimedean Survival Processes, Markov Consistency, ASP Structures

Summary

The Markov consistency of Archimedean survival processes

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2 results

10 - Archimedean Survival Processes, Markov Consistency, ASP Structures

Summary

The Markov consistency of Archimedean survival processes