“On a Classical Risk Model with a Constant Dividend Barrier”, Xiaowen Zhou, October 2005

2006 ◽  
Vol 10 (2) ◽  
pp. 133-139 ◽  
Author(s):  
Beda Chan ◽  
Hans U. Gerber ◽  
Elias S. W. Shiu
Keyword(s):  
Risk Model ◽  
Classical Risk Model ◽  
Constant Dividend Barrier

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.

The density of the time of ruin in the classical risk model with a constant dividend barrier

2013 ◽  
Vol 8 (1) ◽  
pp. 63-78 ◽  
Author(s):  
Shuanming Li ◽  
Yi Lu
Keyword(s):  
Density Function ◽  
Risk Model ◽  
Special Functions ◽  
Laplace Transforms ◽  
Classical Risk Model ◽  
Dividend Payments ◽  
Time Of Ruin ◽  
Constant Dividend Barrier ◽  
The Time Of Ruin ◽  
The Classical Risk Model

AbstractIn this paper, we investigate the density function of the time of ruin in the classical risk model with a constant dividend barrier. When claims are exponentially distributed, we derive explicit expressions for the density function of the time of ruin and its decompositions: the density of the time of ruin without dividend payments and the density of the time of ruin with dividend payments. These densities are obtained based on their Laplace transforms, and expressed in terms of some special functions which are computationally tractable. The Laplace transforms are being inverted using a magnificent tool, the Lagrange inverse formula, developed in Dickson and Willmot (2005). Several numerical examples are given to illustrate our results.

scholarly journals Some Optimal Dividends Problems

2004 ◽  
Vol 34 (01) ◽  
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 A VaR-Type Risk Measure Derived from Cumulative Parisian Ruin for the Classical Risk Model

Risks ◽  
2018 ◽  
Vol 6 (3) ◽  
pp. 85 ◽  
Author(s):  
Mohamed Lkabous ◽  
Jean-François Renaud
Keyword(s):  
Risk Model ◽  
Risk Measures ◽  
Risk Measure ◽  
Short Paper ◽  
Classical Risk Model ◽  
Parisian Ruin ◽  
The Classical Risk Model

In this short paper, we study a VaR-type risk measure introduced by Guérin and Renaud and which is based on cumulative Parisian ruin. We derive some properties of this risk measure and we compare it to the risk measures of Trufin et al. and Loisel and Trufin.

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