Distribution of the Present Value of Dividend Payments in a Lévy Risk Model

2007 ◽  
Vol 44 (02) ◽  
pp. 420-427 ◽  
Author(s):  
Jean-François Renaud ◽  
Xiaowen Zhou
Keyword(s):  
Lévy Processes ◽  
Risk Model ◽  
Levy Processes ◽  
Short Paper ◽  
Insurance Risk ◽  
Present Value ◽  
Dividend Payments ◽  
Insurance Risk Model

In this short paper, we show how fluctuation identities for Lévy processes with no positive jumps yield the distribution of the present value of dividends paid until ruin in a Lévy insurance risk model with a dividend barrier.

scholarly journals Distribution of the Present Value of Dividend Payments in a Lévy Risk Model

2007 ◽  
Vol 44 (2) ◽  
pp. 420-427 ◽  
Author(s):  
Jean-François Renaud ◽  
Xiaowen Zhou
Keyword(s):  
Lévy Processes ◽  
Risk Model ◽  
Levy Processes ◽  
Short Paper ◽  
Insurance Risk ◽  
Present Value ◽  
Dividend Payments ◽  
Insurance Risk Model

In this short paper, we show how fluctuation identities for Lévy processes with no positive jumps yield the distribution of the present value of dividends paid until ruin in a Lévy insurance risk model with a dividend barrier.

scholarly journals Distribution of the Present Value of Dividend Payments in a Lévy Risk Model

2007 ◽  
Vol 44 (02) ◽  
pp. 420-427 ◽  
Author(s):  
Jean-François Renaud ◽  
Xiaowen Zhou
Keyword(s):  
Lévy Processes ◽  
Risk Model ◽  
Levy Processes ◽  
Short Paper ◽  
Insurance Risk ◽  
Present Value ◽  
Dividend Payments ◽  
Insurance Risk Model

In this short paper, we show how fluctuation identities for Lévy processes with no positive jumps yield the distribution of the present value of dividends paid until ruin in a Lévy insurance risk model with a dividend barrier.

scholarly journals The Absolute Ruin Insurance Risk Model with a Threshold Dividend Strategy

Symmetry ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 377 ◽  
Author(s):  
Wenguang Yu ◽  
Yujuan Huang ◽  
Chaoran Cui
Keyword(s):  
Risk Model ◽  
Insurance Companies ◽  
Insurance Company ◽  
Insurance Risk ◽  
Threshold Dividend Strategy ◽  
Dividend Payments ◽  
Absolute Ruin ◽  
The Absolute ◽  
Debit Interest ◽  
Insurance Risk Model

The absolute ruin insurance risk model is modified by including some valuable market economic information factors, such as credit interest, debit interest and dividend payments. Such information is especially important for insurance companies to control risks. We further assume that the insurance company is able to finance and continue to operate when its reserve is negative. We investigate the integro-differential equations for some interest actuarial diagnostics. We also provide numerical examples to explain the effects of relevant parameters on actuarial diagnostics.

scholarly journals General tax Structures and the Lévy Insurance Risk Model

2009 ◽  
Vol 46 (04) ◽  
pp. 1146-1156 ◽  
Author(s):  
Andreas E. Kyprianou ◽  
Xiaowen Zhou
Keyword(s):  
Net Present Value ◽  
Risk Model ◽  
General Structure ◽  
Excursion Theory ◽  
Insurance Risk ◽  
Present Value ◽  
Scale Functions ◽  
Exit Problem ◽  
Tax Payments ◽  
Insurance Risk Model

In the spirit of Albrecher and Hipp (2007), and Albrecher, Renaud, and Zhou (2008) we consider a Lévy insurance risk model with tax payments of a more general structure than in the aforementioned papers, which was also considered in Albrecher, Borst, Boxma, and Resing (2009). In terms of scale functions, we establish three fundamental identities of interest which have stimulated a large volume of actuarial research in recent years. That is to say, the two-sided exit problem, the net present value of tax paid until ruin, as well as a generalized version of the Gerber–Shiu function. The method we appeal to differs from Albrecher and Hipp (2007), and Albrecher, Renaud, and Zhou (2008) in that we appeal predominantly to excursion theory.

scholarly journals General tax Structures and the Lévy Insurance Risk Model

2009 ◽  
Vol 46 (4) ◽  
pp. 1146-1156 ◽  
Author(s):  
Andreas E. Kyprianou ◽  
Xiaowen Zhou
Keyword(s):  
Net Present Value ◽  
Risk Model ◽  
General Structure ◽  
Excursion Theory ◽  
Insurance Risk ◽  
Present Value ◽  
Scale Functions ◽  
Exit Problem ◽  
Tax Payments ◽  
Insurance Risk Model

In the spirit of Albrecher and Hipp (2007), and Albrecher, Renaud, and Zhou (2008) we consider a Lévy insurance risk model with tax payments of a more general structure than in the aforementioned papers, which was also considered in Albrecher, Borst, Boxma, and Resing (2009). In terms of scale functions, we establish three fundamental identities of interest which have stimulated a large volume of actuarial research in recent years. That is to say, the two-sided exit problem, the net present value of tax paid until ruin, as well as a generalized version of the Gerber–Shiu function. The method we appeal to differs from Albrecher and Hipp (2007), and Albrecher, Renaud, and Zhou (2008) in that we appeal predominantly to excursion theory.

scholarly journals Estimating Ruin Probability in an Insurance Risk Model with Stochastic Premium Income Based on the CFS Method

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 982
Author(s):  
Yujuan Huang ◽  
Jing Li ◽  
Hengyu Liu ◽  
Wenguang Yu
Keyword(s):  
Fourier Series ◽  
Ruin Probability ◽  
Risk Model ◽  
Expansion Method ◽  
Nonparametric Estimator ◽  
Insurance Risk ◽  
Numerical Examples ◽  
Complex Fourier Series ◽  
Premium Income ◽  
Insurance Risk Model

This paper considers the estimation of ruin probability in an insurance risk model with stochastic premium income. We first show that the ruin probability can be approximated by the complex Fourier series (CFS) expansion method. Then, we construct a nonparametric estimator of the ruin probability and analyze its convergence. Numerical examples are also provided to show the efficiency of our method when the sample size is finite.

scholarly journals Asymptotic Behavior of Ruin Probabilities in an Insurance Risk Model with Quasi-Asymptotically Independent or Bivariate Regularly Varying-Tailed Main Claim and By-Claim

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-6
Author(s):  
Yang Yang ◽  
Xinzhi Wang ◽  
Xiaonan Su ◽  
Aili Zhang
Keyword(s):  
Asymptotic Behavior ◽  
Risk Model ◽  
Dependence Structure ◽  
Ruin Probabilities ◽  
Insurance Risk ◽  
Main Claim ◽  
Regularly Varying ◽  
Heavy Tailed ◽  
Insurance Risk Model

This paper considers a by-claim risk model under the asymptotical independence or asymptotical dependence structure between each main claim and its by-claim. In the presence of heavy-tailed main claims and by-claims, we derive some asymptotic behavior for ruin probabilities.

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