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The moments of the discounted loss and the discounted dividends for a spectrally negative Lévy risk process

Part of: Stochastic processes Mathematical economics

Published online by Cambridge University Press:  30 March 2016

Esther Frostig
Esther Frostig*
Affiliation:
University of Haifa
*
∗ Postal address: Department of Statistics, University of Haifa, Haifa, 31905, Israel. Email address: frostig@stat.haifa.ac.il
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Abstract

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Consider a spectrally negative risk process where, on ruin, the deficit is immediately paid, and the process restarts from 0. When the process reaches a threshold b, all the surplus above b is paid as dividend. Applying the theory of exit times for a spectrally negative Lévy process and its reflection at the maximum and at the minimum, we obtain recursive formulae for the following moments. (i) The moments of the discounted loss until the process reaches b. This is equivalent to the moments of the discounted dividends in the dual model under the barrier strategy. (ii) The moments of the discounted loss for models with and without a dividend barrier for the infinite horizon. (iii) The moments of the discounted dividends for the infinite horizon.

Keywords

Dividendsbarrier strategycapital injectionexit timesreflected processscale functiondual model

MSC classification

Primary: 60G51: Processes with independent increments; L'evy processes
Secondary: 91B30: Risk theory, insurance
Type
Research Papers
Information
Journal of Applied Probability , Volume 52 , Issue 3 , September 2015 , pp. 665 - 687
Copyright
Copyright © 2015 by the Applied Probability Trust 

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