Dividend-reinsurance strategy in the Sparre Andersen model

2012 ◽  
Vol 29 (2) ◽  
pp. 405-416
Author(s):  
Ji Yang Tan ◽  
Lin Xiao ◽  
Shao Yue Liu ◽  
Xiang Qun Yang
Keyword(s):  
Sparre Andersen Model ◽  
Andersen Model

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

2007 ◽  
Vol 37 (02) ◽  
pp. 203-233 ◽  
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.

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

2007 ◽  
Vol 37 (2) ◽  
pp. 203-233 ◽  
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.

scholarly journals The Joint Density of the Surplus Before and After Ruin in the Sparre Andersen Model

2007 ◽  
Vol 44 (3) ◽  
pp. 695-712 ◽  
Author(s):  
Susan M. Pitts ◽  
Konstadinos Politis
Keyword(s):  
Classical Model ◽  
Joint Density ◽  
Deficit At Ruin ◽  
Sparre Andersen Model ◽  
Andersen Model ◽  
Time Of Ruin ◽  
Collective Risk ◽  
Before And After ◽  
The Deficit At Ruin ◽  
The Time Of Ruin

Gerber and Shiu (1997) have studied the joint density of the time of ruin, the surplus immediately before ruin, and the deficit at ruin in the classical model of collective risk theory. More recently, their results have been generalised for risk models where the interarrival density for claims is nonexponential, but belongs to the Erlang family. Here we obtain generalisations of the Gerber-Shiu (1997) results that are valid in a general Sparre Andersen model, i.e. for any interclaim density. In particular, we obtain a generalisation of the key formula in that paper. Our results are made more concrete for the case where the distribution between claim arrivals is phase-type or the integrated tail distribution associated with the claim size distribution belongs to the class of subexponential distributions. Furthermore, we obtain conditions for finiteness of the joint moments of the surplus before ruin and the deficit at ruin in the Sparre Andersen model.

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