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Optimal barrier strategy for spectrally negative Lévy process discounted by a class of exponential Lévy processes

Published online by Cambridge University Press:  27 February 2018

Huanqun Jiang Open the ORCID record for Huanqun Jiang [Opens in a new window]
Huanqun Jiang*
Affiliation:
Department of Mathematics, Oregon State University, Corvallis, OR 97331, USA
*
*Correspondence to: Huanqun Jiang, Department of Mathematics, Oregon State University, Corvallis, OR 97331, USA. Tel: (541)737 4686. E-mail: jiangh@math.oregonstate.edu
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Abstract

In this paper, we extend the optimality of the barrier strategy for the dividend payment problem to the setting that the underlying surplus process is a spectrally negative Lévy process and the discounting factor is an exponential Lévy process. The proof of the main result uses the fluctuation identities of spectrally negative Lévy processes. This extends recent results of Eisenberg for the case where the accumulated interest rate and surplus process are independent Brownian motions with drift.

Keywords

Optimal barrier strategySpectrally negative Lévy processFluctuation identitiesExponential Lévy process
Type
Paper
Information
Annals of Actuarial Science , Volume 12 , Issue 2 , September 2018 , pp. 326 - 337
Copyright
© Institute and Faculty of Actuaries 2018 

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