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ON THE OPTIMAL DIVIDEND PROBLEM FOR A SPECTRALLY POSITIVE LÉVY PROCESS

Published online by Cambridge University Press:  10 April 2014

Chuancun Yin ,
Yuzhen Wen  and
Yongxia Zhao
Chuancun Yin*
Affiliation:
School of Mathematical Sciences, Qufu Normal UniversityShandong 273165, P.R. China
Yuzhen Wen
Affiliation:
School of Mathematical Sciences, Qufu Normal UniversityShandong 273165, P.R. China
Yongxia Zhao
Affiliation:
School of Mathematical Sciences, Qufu Normal UniversityShandong 273165, P.R. China
*
E-Mail: [email protected]
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Abstract

In this paper we study the optimal dividend problem for a company whose surplus process evolves as a spectrally positive Lévy process before dividends are deducted. This model includes the dual model of the classical risk model and the dual model with diffusion as special cases. We assume that dividends are paid to the shareholders according to an admissible strategy whose dividend rate is bounded by a constant. The objective is to find a dividend policy so as to maximize the expected discounted value of dividends which are paid to the shareholders until the company is ruined. We show that the optimal dividend strategy is formed by a threshold strategy.

Keywords

Threshold strategydual modeloptimal dividend strategyscale functionsspectrally positive Lévy processstochastic control
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 44 , Issue 3 , September 2014 , pp. 635 - 651
Copyright
Copyright © ASTIN Bulletin 2014 

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