Dividend payments in the classical risk model under absolute ruin with debit interest

2009 ◽  
Vol 25 (3) ◽  
pp. 247-262 ◽  
Author(s):  
Chunwei Wang ◽  
Chuancun Yin
Keyword(s):  
Risk Model ◽  
Classical Risk Model ◽  
Dividend Payments ◽  
Absolute Ruin ◽  
Debit Interest ◽  
The Classical Risk Model

scholarly journals On Periodic Dividends for the Classical Risk Model with Debit Interest

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Hua Dong ◽  
Xianghua Zhao
Keyword(s):  
Differential Equations ◽  
Risk Model ◽  
Classical Risk Model ◽  
Arrival Times ◽  
Numerical Examples ◽  
Dividend Payments ◽  
Poisson Arrival ◽  
Optimal Dividend ◽  
Debit Interest ◽  
The Classical Risk Model

A periodic dividend problem is studied in this paper. We assume that dividend payments are made at a sequence of Poisson arrival times, and ruin is continuously monitored. First of all, three integro-differential equations for the expected discounted dividends are obtained. Then, we investigate the explicit expressions for the expected discounted dividends, and the optimal dividend barrier is given for exponential claims. A similar study on a generalized Gerber–Shiu function involving the absolute time is also performed. To demonstrate the existing results, we give some numerical examples.

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 The Absolute Ruin Insurance Risk Model with a Threshold Dividend Strategy

Symmetry ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 377 ◽  
Author(s):  
Wenguang Yu ◽  
Yujuan Huang ◽  
Chaoran Cui
Keyword(s):  
Risk Model ◽  
Insurance Companies ◽  
Insurance Company ◽  
Insurance Risk ◽  
Threshold Dividend Strategy ◽  
Dividend Payments ◽  
Absolute Ruin ◽  
The Absolute ◽  
Debit Interest ◽  
Insurance Risk Model

The absolute ruin insurance risk model is modified by including some valuable market economic information factors, such as credit interest, debit interest and dividend payments. Such information is especially important for insurance companies to control risks. We further assume that the insurance company is able to finance and continue to operate when its reserve is negative. We investigate the integro-differential equations for some interest actuarial diagnostics. We also provide numerical examples to explain the effects of relevant parameters on actuarial diagnostics.

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.

An adaptive premium policy with a Bayesian motivation in the classical risk model

2012 ◽  
Vol 51 (2) ◽  
pp. 370-378 ◽  
Author(s):  
David Landriault ◽  
Christiane Lemieux ◽  
Gordon E. Willmot
Keyword(s):  
Risk Model ◽  
Classical Risk Model ◽  
The Classical Risk Model
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