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On a bivariate risk process with a dividend barrier strategy

Published online by Cambridge University Press:  22 July 2014

Luyin Liu  and
Eric C. K. Cheung
Luyin Liu*
Affiliation:
Department of Statistics and Actuarial Science, University of Hong Kong, Pokfulam, Hong Kong
Eric C. K. Cheung*
Affiliation:
Department of Statistics and Actuarial Science, University of Hong Kong, Pokfulam, Hong Kong
*
*Correspondence to: Luyin Liu and Eric C. K. Cheung, Department of Statistics and Actuarial Science, University of Hong Kong, Pokfulam, Hong Kong. Tel: (852) 2857-8315; Fax: (852) 2858-9041; E-mail: kidaliu@gmail.com; eckc@hku.hk
*Correspondence to: Luyin Liu and Eric C. K. Cheung, Department of Statistics and Actuarial Science, University of Hong Kong, Pokfulam, Hong Kong. Tel: (852) 2857-8315; Fax: (852) 2858-9041; E-mail: kidaliu@gmail.com; eckc@hku.hk
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Abstract

In this paper, we study a continuous-time bivariate risk process in which each individual line of business implements a dividend barrier strategy. The insurance portfolios of the two insurers are correlated as they are subject to common shocks that induce dependent claims. To analyse the expected discounted dividends until the joint ruin time of the bivariate process (i.e. exit from the positive quadrant), we propose a discrete-time counterpart of the model and apply a bivariate extension of the Dickson−Waters discretisation with the use of a bivariate Panjer-type recursion. Detailed numerical examples under different dependencies via common shocks, copulas and proportional reinsurance are discussed, and applications to optimal problems in reinsurance, capital allocation and dividends are given. It is also illustrated that the optimal pair of dividend barriers maximising the dividend function is dependent on the initial surplus levels. A modified type of dividend barrier strategy is proposed towards the end.

Keywords

Bivariate risk processDiscretisationDividend barrier strategyCopulasCapital allocationProportional reinsurance
Type
Papers
Information
Annals of Actuarial Science , Volume 9 , Issue 1 , March 2015 , pp. 3 - 35
Copyright
© Institute and Faculty of Actuaries 2014 

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