scholarly journals Randomized observation periods for the compound Poisson risk model: the discounted penalty function

2013 ◽  
Vol 2013 (6) ◽  
pp. 424-452 ◽  
Author(s):  
Hansjörg Albrecher ◽  
Eric C.K. Cheung ◽  
Stefan Thonhauser
Keyword(s):  
Penalty Function ◽  
Risk Model ◽  
Compound Poisson ◽  
Compound Poisson Risk Model ◽  
Discounted Penalty Function ◽  
Poisson Risk Model

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.

Moments of Discounted Dividends for a Threshold Strategy in the Compound Poisson Risk Model

2008 ◽  
Vol 12 (3) ◽  
pp. 299-318 ◽  
Author(s):  
Eric C. K. Cheung ◽  
David C. M. Dickson ◽  
Steve Drekic
Keyword(s):  
Risk Model ◽  
Threshold Strategy ◽  
Compound Poisson ◽  
Compound Poisson Risk Model ◽  
Poisson Risk Model

scholarly journals Dynamic Proportional Reinsurance and Approximations for Ruin Probabilities in the Two-Dimensional Compound Poisson Risk Model

2012 ◽  
Vol 2012 ◽  
pp. 1-26 ◽  
Author(s):  
Yan Li ◽  
Guoxin Liu
Keyword(s):  
Ruin Probability ◽  
Risk Model ◽  
Optimal Strategies ◽  
Proportional Reinsurance ◽  
Two Dimensional ◽  
Compound Poisson ◽  
Compound Poisson Risk Model ◽  
Optimal Value ◽  
Hamilton Jacobi Bellman ◽  
Poisson Risk Model

We consider the dynamic proportional reinsurance in a two-dimensional compound Poisson risk model. The optimization in the sense of minimizing the ruin probability which is defined by the sum of subportfolio is being ruined. Via the Hamilton-Jacobi-Bellman approach we find a candidate for the optimal value function and prove the verification theorem. In addition, we obtain the Lundberg bounds and the Cramér-Lundberg approximation for the ruin probability and show that as the capital tends to infinity, the optimal strategies converge to the asymptotically optimal constant strategies. The asymptotic value can be found by maximizing the adjustment coefficient.

The Compound Poisson Risk Model with Interest and a Threshold Strategy

2009 ◽  
Vol 25 (2) ◽  
pp. 197-220 ◽  
Author(s):  
Haili Yuan ◽  
Yijun Hu
Keyword(s):  
Risk Model ◽  
Threshold Strategy ◽  
Compound Poisson ◽  
Compound Poisson Risk Model ◽  
Poisson Risk Model

On the compound Poisson risk model with dependence and a threshold dividend strategy

2013 ◽  
Vol 83 (9) ◽  
pp. 1998-2006 ◽  
Author(s):  
Yafeng Shi ◽  
Peng Liu ◽  
Chunsheng Zhang
Keyword(s):  
Risk Model ◽  
Compound Poisson ◽  
Threshold Dividend Strategy ◽  
Compound Poisson Risk Model ◽  
Poisson Risk Model

scholarly journals On a perturbed by diffusion compound Poisson risk model with delayed claims and multi-layer dividend strategy

2013 ◽  
Vol 253 ◽  
pp. 26-50 ◽  
Author(s):  
Stathis Chadjiconstantinidis ◽  
Apostolos D. Papaioannou
Keyword(s):  
Risk Model ◽  
Compound Poisson ◽  
Compound Poisson Risk Model ◽  
Poisson Risk Model

The compound Poisson risk model under a mixed dividend strategy

2017 ◽  
Vol 315 ◽  
pp. 1-12 ◽  
Author(s):  
Zhimin Zhang ◽  
Xiao Han
Keyword(s):  
Risk Model ◽  
Compound Poisson ◽  
Compound Poisson Risk Model ◽  
Poisson Risk Model
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