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On the finiteness and tails of perpetuities under a Lamperti–Kiu MAP

Part of: Markov processes Stochastic processes Mathematical economics

Published online by Cambridge University Press:  22 November 2021

Larbi Alili  and
David Woodford
Larbi Alili*
Affiliation:
University of Warwick
David Woodford*
Affiliation:
University of Warwick
*
*Postal address: The University of Warwick, Coventry CV47AL, UK.
*Postal address: The University of Warwick, Coventry CV47AL, UK.
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Abstract

Consider a Lamperti–Kiu Markov additive process $(J, \xi)$ on $\{+, -\}\times\mathbb R\cup \{-\infty\}$, where J is the modulating Markov chain component. First we study the finiteness of the exponential functional and then consider its moments and tail asymptotics under Cramér’s condition. In the strong subexponential case we determine the subexponential tails of the exponential functional under some further assumptions.

Keywords

Markov additive processLamperti–Kiu representationself-similar Markov processperpetuity

MSC classification

Primary: 60G18: Self-similar processes
Secondary: 60J45: Probabilistic potential theory 91B70: Stochastic models 91B30: Risk theory, insurance
Type
Original Article
Information
Journal of Applied Probability , Volume 58 , Issue 4 , December 2021 , pp. 1086 - 1113
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Applied Probability Trust

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