The Gerber–Shiu discounted penalty function for classical risk model with a two-step premium rate

2006 ◽  
Vol 76 (12) ◽  
pp. 1211-1218 ◽  
Author(s):  
H.Y. Zhang ◽  
M. Zhou ◽  
J.Y. Guo
Keyword(s):  
Penalty Function ◽  
Risk Model ◽  
Classical Risk Model ◽  
Premium Rate ◽  
Discounted Penalty Function

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.

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.

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 Gerber-Shiu Function in a Discrete-time Risk Model with Dividend Strategy

2021 ◽  
pp. 97-110
Author(s):  
Junqing Huang ◽  
Zhenhua Bao
Keyword(s):  
General Theory ◽  
Discrete Time ◽  
Difference Equations ◽  
Penalty Function ◽  
Risk Model ◽  
Fundamental Equation ◽  
Numerical Examples ◽  
Premium Rate ◽  
Discounted Penalty Function ◽  
Constant Dividend Barrier

In this paper, a discrete-time risk model with dividend strategy and a general premium rate is considered. Under such a strategy, once the insurer’s surplus hits a constant dividend barrier , dividends are paid off to shareholders at  instantly. Using the roots of a generalization of Lundberg’s fundamental equation and the general theory on difference equations, two difference equations for the Gerber-Shiu discounted penalty function are derived and solved. The analytic results obtained are utilized to derive the probability of ultimate ruin when the claim sizes is a mixture of two geometric distributions. Numerical examples are also given to illustrate the applicability of the results obtained.

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