On a discrete-time risk model with time-dependent claims and impulsive dividend payments

Abstract

A discrete-time risk model with a mathematically tractable dependence structure between interclaim times and claim sizes is considered in the presence of an impulsive dividend strategy. Under such a strategy, once the insurer's reserve upcrosses the level b, the excess of the reserve over $a(a\le b)$ is paid off as dividends. We derive difference equations for both the expected discounted penalty function and the expected present value of dividend payments. Solution procedures for these difference equations are provided. When the joint distribution of the interclaim time and claim size is a finite mixture of bivariate geometric distributions, closed-form expressions are given. Numerical results for several sets of parameters are also provided to illustrate the applicability of the results obtained.

Keywords:

• Discrete-time risk model
• dependence structure
• dividend strategy
• defective renewal equation
• bivariate geometric distribution

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Correction

Acknowledgements

The authors would like to thank two anonymous referees; their helpful comments led to several improvements in the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article was originally published with errors, which have now been corrected in the online version. Please see Correction (https://doi.org/10.1080/03461238.2020.1742478).

Additional information

Funding

This research was supported by NSFC (project No. 61673225).