Dividend payments with a threshold strategy in a Markov-dependent risk model

2011 ◽  
Vol 16 (1) ◽  
pp. 11-15 ◽  
Author(s):  
Juan Liu ◽  
Jiancheng Xu ◽  
Hongchang Hu
Keyword(s):  
Risk Model ◽  
Threshold Strategy ◽  
Dividend Payments

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 Optimal Dividend and Capital Injection Strategies for a Risk Model under Force of Interest

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Ying Fang ◽  
Zhongfeng Qu
Keyword(s):  
Risk Model ◽  
Risk Process ◽  
Insurance Company ◽  
Threshold Strategy ◽  
Dividend Payments ◽  
Optimal Dividend ◽  
Optimal Injection ◽  
Force Of Interest ◽  
Capital Injections ◽  
Injection Strategies

As a generalization of the classical Cramér-Lundberg risk model, we consider a risk model including a constant force of interest in the present paper. Most optimal dividend strategies which only consider the processes modeling the surplus of a risk business are absorbed at 0. However, in many cases, negative surplus does not necessarily mean that the business has to stop. Therefore, we assume that negative surplus is not allowed and the beneficiary of the dividends is required to inject capital into the insurance company to ensure that its risk process stays nonnegative. For this risk model, we show that the optimal dividend strategy which maximizes the discounted dividend payments minus the penalized discounted capital injections is a threshold strategy for the case of the dividend payout rate which is bounded by some positive constant and the optimal injection strategy is to inject capitals immediately to make the company's assets back to zero when the surplus of the company becomes negative.

scholarly journals ON THE OPTIMAL DIVIDEND PROBLEM FOR A SPECTRALLY POSITIVE LÉVY PROCESS

2014 ◽  
Vol 44 (3) ◽  
pp. 635-651 ◽  
Author(s):  
Chuancun Yin ◽  
Yuzhen Wen ◽  
Yongxia Zhao
Keyword(s):  
Lévy Process ◽  
Risk Model ◽  
Levy Process ◽  
Dual Model ◽  
Threshold Strategy ◽  
Classical Risk Model ◽  
Surplus Process ◽  
Optimal Dividend ◽  
Special Cases ◽  
The Classical Risk Model

AbstractIn 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.

scholarly journals Some Optimal Dividends Problems

2004 ◽  
Vol 34 (1) ◽  
pp. 49-74 ◽  
Author(s):  
David C.M. Dickson ◽  
Howard R. Waters
Keyword(s):  
Discrete Time ◽  
Risk Model ◽  
Present Value ◽  
Classical Risk Model ◽  
Optimal Dividends ◽  
Surplus Process ◽  
Dividend Payments ◽  
Constant Dividend Barrier ◽  
De Finetti ◽  
The Classical Risk Model

We consider a situation originally discussed by De Finetti (1957) in which a surplus process is modified by the introduction of a constant dividend barrier. We extend some known results relating to the distribution of the present value of dividend payments until ruin in the classical risk model and show how a discrete time risk model can be used to provide approximations when analytic results are unavailable. We extend the analysis by allowing the process to continue after ruin.

scholarly journals On a Dual Model with Barrier Strategy

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Yuzhen Wen ◽  
Chuancun Yin
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Generating Function ◽  
Risk Model ◽  
Moment Generating Function ◽  
Dual Model ◽  
Barrier Strategy ◽  
Dividend Payments ◽  
The Moment

We consider the dual of the generalized Erlang(n)risk model with a barrier dividend strategy. We derive integro-differential equations with boundary conditions satisfied by the expectation of the sum of discounted dividends until ruin and the moment-generating function of the discounted dividend payments until ruin, respectively. The results are illustrated by several examples.

Sign in / Sign up

Export Citation Format

Share Document