The gerber-shiu expected discounted penalty function for Lévy insurance risk processes

2010 ◽  
Vol 26 (4) ◽  
pp. 575-586 ◽  
Author(s):  
Xiang-hua Zhao ◽  
Chuan-cun Yin
Keyword(s):  
Penalty Function ◽  
Insurance Risk ◽  
Expected Discounted Penalty Function ◽  
Discounted Penalty Function ◽  
Risk Processes ◽  
Expected Discounted Penalty

scholarly journals Estimating the Expected Discounted Penalty Function in a Compound Poisson Insurance Risk Model with Mixed Premium Income

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 305 ◽  
Author(s):  
Yunyun Wang ◽  
Wenguang Yu ◽  
Yujuan Huang ◽  
Xinliang Yu ◽  
Hongli Fan
Keyword(s):  
Penalty Function ◽  
Risk Model ◽  
Insurance Risk ◽  
Compound Poisson ◽  
Expected Discounted Penalty Function ◽  
Fourier Cosine ◽  
Discounted Penalty Function ◽  
Premium Income ◽  
Expected Discounted Penalty ◽  
Insurance Risk Model

In this paper, we consider an insurance risk model with mixed premium income, in which both constant premium income and stochastic premium income are considered. We assume that the stochastic premium income process follows a compound Poisson process and the premium sizes are exponentially distributed. A new method for estimating the expected discounted penalty function by Fourier-cosine series expansion is proposed. We show that the estimation is easily computed, and it has a fast convergence rate. Some numerical examples are also provided to show the good properties of the estimation when the sample size is finite.

Sign in / Sign up

Export Citation Format

Share Document