scholarly journals The Gerber-Shiu Discounted Penalty Function of Sparre Andersen Risk Model with a Constant Dividend Barrier

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Yujuan Huang ◽  
Wenguang Yu
Keyword(s):  
Differential Equation ◽  
Exponential Distribution ◽  
Penalty Function ◽  
Risk Model ◽  
Integro Differential Equation ◽  
Numerical Example ◽  
N Distribution ◽  
Discounted Penalty Function ◽  
Constant Dividend Barrier ◽  
Sparre Andersen Risk Model

This paper constructs a Sparre Andersen risk model with a constant dividend barrier in which the claim interarrival distribution is a mixture of an exponential distribution and an Erlang(n) distribution. We derive the integro-differential equation satisfied by the Gerber-Shiu discounted penalty function of this risk model. Finally, we provide a numerical example.

On a Risk Model with Dependence between Claim Sizes and Claim Intervals under a Linear Dividend Barrier and Stochastic Interest

2010 ◽  
Vol 26-28 ◽  
pp. 598-602
Author(s):  
Ting Shan Song
Keyword(s):  
Differential Equation ◽  
Penalty Function ◽  
Risk Model ◽  
Penalty Functions ◽  
Integro Differential Equation ◽  
Linearly Independent ◽  
Stochastic Interest ◽  
Discounted Penalty Function

The risk model with interclaim-dependent claim sizes is studied in the presence of a linear dividend barrier and stochastic interest. An integro-differential equation for some Gerber-Shiu discounted penalty functions is derived. We show that its solution can be expressed as the solution to the Gerber-Shiu discounted penalty function in the same risk model with the absence of a barrier and a combination of two linearly independent solutions to the associated homogeneous integro-differential equation.

The Markov Risk Model under Stochastic Discount Interest Force

2011 ◽  
Vol 179-180 ◽  
pp. 1080-1085
Author(s):  
Yu Juan Huang ◽  
Chun Ming Zhang
Keyword(s):  
Differential Equation ◽  
Penalty Function ◽  
Risk Model ◽  
Standard Wiener Process ◽  
Exponential Distributions ◽  
Expected Discounted Penalty Function ◽  
Geometric Process ◽  
Interest Force ◽  
Discounted Penalty Function ◽  
Expected Discounted Penalty

We investigate the expected discounted penalty function in which the discount interest process is driven by markov process. We obtain the integro-differential equation satisfied by the expected discounted penalty function when interest process is perturbed by standard Wiener process and Poisson-Geometric process. A system of Laplace transforms of the expected discounted penalty function, given the initial environment state, is established from a system of integro-differential equations. One example is given with claim sizes that have exponential distributions.

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.

scholarly journals A Note on a Generalized Gerber–Shiu Discounted Penalty Function for a Compound Poisson Risk Model

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 891 ◽  
Author(s):  
Jiechang Ruan ◽  
Wenguang Yu ◽  
Ke Song ◽  
Yihan Sun ◽  
Yujuan Huang ◽  
...  
Keyword(s):  
Laplace Transform ◽  
Exponential Distribution ◽  
Penalty Function ◽  
Risk Model ◽  
Recursive Method ◽  
Ruin Time ◽  
Compound Poisson ◽  
Compound Poisson Risk Model ◽  
Discounted Penalty Function ◽  
Poisson Risk Model

In this paper, we propose a new generalized Gerber–Shiu discounted penalty function for a compound Poisson risk model, which can be used to study the moments of the ruin time. First, by taking derivatives with respect to the original Gerber–Shiu discounted penalty function, we construct a relation between the original Gerber–Shiu discounted penalty function and our new generalized Gerber–Shiu discounted penalty function. Next, we use Laplace transform to derive a defective renewal equation for the generalized Gerber–Shiu discounted penalty function, and give a recursive method for solving the equation. Finally, when the claim amounts obey the exponential distribution, we give some explicit expressions for the generalized Gerber–Shiu discounted penalty function. Numerical illustrations are also given to study the effect of the parameters on the generalized Gerber–Shiu discounted penalty function.

scholarly journals The Gerber-Shiu Expected Penalty Function for the Risk Model with Dependence and a Constant Dividend Barrier

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Donghai Liu ◽  
Zaiming Liu ◽  
Dan Peng
Keyword(s):  
Linear Combination ◽  
Penalty Function ◽  
Integrodifferential Equation ◽  
Risk Model ◽  
Dependence Structure ◽  
Claim Amount ◽  
Compound Poisson ◽  
Compound Poisson Risk Model ◽  
Discounted Penalty Function ◽  
Constant Dividend Barrier

We consider a compound Poisson risk model with dependence and a constant dividend barrier. A dependence structure between the claim amount and the interclaim time is introduced through a Farlie-Gumbel-Morgenstern copula. An integrodifferential equation for the Gerber-Shiu discounted penalty function is derived. We also solve the integrodifferential equation and show that the solution is a linear combination of the Gerber-Shiu function with no barrier and the solution of an associated homogeneous integrodifferential equation.

Sign in / Sign up

Export Citation Format

Share Document