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

Deficit distributions at ruin in a regime-switching Sparre Andersen model AbstractIn this paper, we investigate deficit distributions at ruin ina regime-switching Sparre Andersen model. A Markov chain isassumed to switch the amount and/or respective wait time distributions ofclaims while the insurer can adjust the premiums in response.Special attention is paid to an operator 𝐋{\mathbf{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{\mathbf{L}}on the vector of functionsbeing identically equal to zero. Moreover, in the case of infinitehorizon, the deficit distributions at ruin are shown to be a fixed point of 𝐋{\mathbf{L}}.Upper bounds for the vector of deficit distributions at ruin are also proven. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Applied Analysis de Gruyter

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

, Volume 24 (1): 9 – Jun 1, 2018
9 pages

/lp/degruyter/deficit-distributions-at-ruin-in-a-regime-switching-sparre-andersen-AjMI6gozPI
Publisher
de Gruyter
© 2018 Walter de Gruyter GmbH, Berlin/Boston
ISSN
1869-6082
eISSN
1869-6082
D.O.I.
10.1515/jaa-2018-0010
Publisher site
See Article on Publisher Site

### Abstract

AbstractIn this paper, we investigate deficit distributions at ruin ina regime-switching Sparre Andersen model. A Markov chain isassumed to switch the amount and/or respective wait time distributions ofclaims while the insurer can adjust the premiums in response.Special attention is paid to an operator 𝐋{\mathbf{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{\mathbf{L}}on the vector of functionsbeing identically equal to zero. Moreover, in the case of infinitehorizon, the deficit distributions at ruin are shown to be a fixed point of 𝐋{\mathbf{L}}.Upper bounds for the vector of deficit distributions at ruin are also proven.

### Journal

Journal of Applied Analysisde Gruyter

Published: Jun 1, 2018

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