The classical risk model with a constant dividend barrier: analysis of the Gerber–Shiu discounted penalty function

2003 ◽  
Vol 33 (3) ◽  
pp. 551-566 ◽  
Author(s):  
X. Sheldon Lin ◽  
Gordon E. Willmot ◽  
Steve Drekic
Keyword(s):  
Penalty Function ◽  
Risk Model ◽  
Classical Risk Model ◽  
Barrier Analysis ◽  
Discounted Penalty Function ◽  
Constant Dividend Barrier ◽  
The Classical Risk Model

scholarly journals On the Expected Discounted Penalty Function for the Classical Risk Model with Potentially Delayed Claims and Random Incomes

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Huiming Zhu ◽  
Ya Huang ◽  
Xiangqun Yang ◽  
Jieming Zhou
Keyword(s):  
Penalty Function ◽  
Risk Model ◽  
Claim Amount ◽  
Classical Risk Model ◽  
Main Claim ◽  
Expected Discounted Penalty Function ◽  
The Laplace Transform ◽  
Discounted Penalty Function ◽  
The Classical Risk Model ◽  
Expected Discounted Penalty

We focus on the expected discounted penalty function of a compound Poisson risk model with random incomes and potentially delayed claims. It is assumed that each main claim will produce a byclaim with a certain probability and the occurrence of the byclaim may be delayed depending on associated main claim amount. In addition, the premium number process is assumed as a Poisson process. We derive the integral equation satisfied by the expected discounted penalty function. Given that the premium size is exponentially distributed, the explicit expression for the Laplace transform of the expected discounted penalty function is derived. Finally, for the exponential claim sizes, we present the explicit formula for the expected discounted penalty function.

On the Discounted Penalty Function for Claims Having Mixed Exponential

2006 ◽  
Vol 11 (4) ◽  
pp. 413-426
Author(s):  
J. Šiaulys ◽  
J. Kočetova
Keyword(s):  
Poisson Process ◽  
Infinite Series ◽  
Penalty Function ◽  
Risk Model ◽  
Classical Risk Model ◽  
Ruin Time ◽  
Discounted Penalty Function ◽  
Force Of Interest ◽  
The Classical Risk Model ◽  
Mixed Exponential Distribution

It is considered the classical risk model with mixed exponential claim sizes. Using known results it is obtained the explicit expression of the GerberShiu discounted penalty function ψ(x,δ) = E e −δT 1(T < ∞) , by some infinite series. Here δ > 0 is the force of interest, x – the initial reserve and T – ruin time. The dependance of the discounted penalty function on the main parameters x, θ, λ, δ, α, σ, ν is presented in diagrams, where λ > 0 is the parameter of Poisson process, θ > 0 is the safety loading coefficient, 0 ≤ α ≤ 1 and σ, ν > 0 are the parameters of the mixed exponential distribution

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.

Improvement to the Expected Discounted Penalty Function for a Classical Risk Model with a Threshold Dividend Strategy

2010 ◽  
Vol 29-32 ◽  
pp. 1150-1155
Author(s):  
Wen Guang Yu ◽  
Zhi Liu
Keyword(s):  
Differential Equation ◽  
Stochastic Process ◽  
Penalty Function ◽  
Risk Model ◽  
Classical Risk Model ◽  
Expected Discounted Penalty Function ◽  
Threshold Dividend Strategy ◽  
Interest Force ◽  
Discounted Penalty Function ◽  
Expected Discounted Penalty

In this paper, we study the expected discounted penalty function for a classical risk model in which a threshold dividend strategy is used for a classical risk model and the discount interest force process is not a constant, but a stochastic process driven by Poisson process and Wiener process. In this model, we derive and solve an integro-differential equation for the expected discounted penalty function.

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.

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