“The Time of Recovery and the Maximum Severity of Ruin in a Sparre Andersen Model,” Shuanming Li, October 2008

For the classical Cramér-Lundberg risk model, a dividend strategy of threshold type has recently been suggested in the literature. This strategy consists of paying out part of the premium income as dividends to shareholders whenever the free surplus is above a given threshold level. In contrast to the well-known horizontal barrier strategy, the threshold strategy can lead to a positive infinite-horizon survival probability, with reduced profit in terms of dividend payments. In this paper we extend several of these results to a Sparre Andersen model with generalized Erlang(n)-distributed interclaim times. Furthermore, we compare the performance of the threshold strategy to a linear dividend barrier model. In particular, (partial) integro-differential equations for the corresponding ruin probabilities and expected discounted dividend payments are provided for both models and explicitly solved for n = 2 and exponentially distributed claim amounts. Finally, the explicit solutions are used to identify parameter sets for which one strategy outperforms the other and vice versa.

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An optimal dividend strategy in the discrete Sparre Andersen model with bounded dividend rates

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2013.08.029 ◽

2014 ◽

Vol 258 ◽

pp. 1-16 ◽

Cited By ~ 6

Author(s):

Jiyang Tan ◽

Pingtian Yuan ◽

Yangjin Cheng ◽

Ziqiang Li

Keyword(s):

Sparre Andersen Model ◽

Andersen Model ◽

Optimal Dividend ◽

Optimal Dividend Strategy

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On Exact Solutions for Dividend Strategies of Threshold and Linear Barrier Type in a Sparre Andersen Model

Astin Bulletin ◽

10.1017/s0515036100014847 ◽

2007 ◽

Vol 37 (2) ◽

pp. 203-233 ◽

Cited By ~ 10

Author(s):

Hansjörg Albrecher ◽

Jürgen Hartinger ◽

Stefan Thonhauser

Keyword(s):

Risk Model ◽

Infinite Horizon ◽

Threshold Level ◽

Threshold Strategy ◽

Sparre Andersen Model ◽

Dividend Payments ◽

Andersen Model ◽

Linear Barrier ◽

Barrier Type ◽

Premium Income

For the classical Cramér-Lundberg risk model, a dividend strategy of threshold type has recently been suggested in the literature. This strategy consists of paying out part of the premium income as dividends to shareholders whenever the free surplus is above a given threshold level. In contrast to the well-known horizontal barrier strategy, the threshold strategy can lead to a positive infinite-horizon survival probability, with reduced profit in terms of dividend payments. In this paper we extend several of these results to a Sparre Andersen model with generalized Erlang(n)-distributed interclaim times. Furthermore, we compare the performance of the threshold strategy to a linear dividend barrier model. In particular, (partial) integro-differential equations for the corresponding ruin probabilities and expected discounted dividend payments are provided for both models and explicitly solved for n = 2 and exponentially distributed claim amounts. Finally, the explicit solutions are used to identify parameter sets for which one strategy outperforms the other and vice versa.

Download Full-text