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Deficit distributions at ruin in a regime-switching Sparre Andersen model

  • Lesław Gajek EMAIL logo and Marcin Rudź
Published/Copyright: May 23, 2018

Abstract

In this paper, we investigate deficit distributions at ruin in a regime-switching Sparre Andersen model. A Markov chain is assumed to switch the amount and/or respective wait time distributions of claims while the insurer can adjust the premiums in response. Special attention is paid to an operator 𝐋 generated by the risk process. We show that the deficit distributions at ruin during n periods, given the state of the Markov chain at time zero, form a vector of functions, which is the n-th iteration of 𝐋 on the vector of functions being identically equal to zero. Moreover, in the case of infinite horizon, the deficit distributions at ruin are shown to be a fixed point of 𝐋. Upper bounds for the vector of deficit distributions at ruin are also proven.

MSC 2010: 91B30; 60J20

Funding statement: The research was supported by the National Science Centre, Poland (2014/13/B/HS4/03222).

Acknowledgements

The authors thank the reviewer for helpful comments.

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Received: 2017-2-21
Revised: 2018-3-14
Accepted: 2018-4-17
Published Online: 2018-5-23
Published in Print: 2018-6-1

© 2018 Walter de Gruyter GmbH, Berlin/Boston

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