scholarly journals Uniform Asymptotics for a Delay-Claims Risk Model with Constant Force of Interest and By-Claims Arriving according to a Counting Process

2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
Qingwu Gao ◽  
Xijun Liu

The insurance risk model involving main claims and by-claims has been traditionally studied under the assumption that every main claim may be accompanied with a by-claim occurring after a period of delay, but in reality each main claim can cause many by-claims arriving according to a counting process. To this end, we construct a new insurance risk model that is also perturbed by diffusion with constant force of interest. In the presence of heavy tails and dependence structures among modelling components, we obtain some asymptotic results for the finite-time ruin probability and the tail probability of discounted aggregate claims, where the results hold uniformly for all times in a finite or infinite interval.

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-6
Author(s):  
Yang Yang ◽  
Xinzhi Wang ◽  
Xiaonan Su ◽  
Aili Zhang

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.


Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 982
Author(s):  
Yujuan Huang ◽  
Jing Li ◽  
Hengyu Liu ◽  
Wenguang Yu

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.


2010 ◽  
Vol 47 (2) ◽  
pp. 323-334 ◽  
Author(s):  
Dimitrios G. Konstantinides ◽  
Kai W. Ng ◽  
Qihe Tang

In this paper we consider the probabilities of finite- and infinite-time absolute ruins in the renewal risk model with constant premium rate and constant force of interest. In the particular case of the compound Poisson model, explicit asymptotic expressions for the finite- and infinite-time absolute ruin probabilities are given. For the general renewal risk model, we present an asymptotic expression for the infinite-time absolute ruin probability. Conditional distributions of Poisson processes and probabilistic techniques regarding randomly weighted sums are employed in the course of this study.


Risks ◽  
2018 ◽  
Vol 6 (4) ◽  
pp. 110 ◽  
Author(s):  
Sooie-Hoe Loke ◽  
Enrique Thomann

In this paper, a dual risk model under constant force of interest is considered. The ruin probability in this model is shown to satisfy an integro-differential equation, which can then be written as an integral equation. Using the collocation method, the ruin probability can be well approximated for any gain distributions. Examples involving exponential, uniform, Pareto and discrete gains are considered. Finally, the same numerical method is applied to the Laplace transform of the time of ruin.


1994 ◽  
Vol 26 (02) ◽  
pp. 404-422 ◽  
Author(s):  
Paul Embrechts ◽  
Hanspeter Schmidli

The theory of piecewise-deterministic Markov processes is used in order to investigate insurance risk models where borrowing, investment and inflation are present.


2010 ◽  
Vol 47 (02) ◽  
pp. 323-334 ◽  
Author(s):  
Dimitrios G. Konstantinides ◽  
Kai W. Ng ◽  
Qihe Tang

In this paper we consider the probabilities of finite- and infinite-time absolute ruins in the renewal risk model with constant premium rate and constant force of interest. In the particular case of the compound Poisson model, explicit asymptotic expressions for the finite- and infinite-time absolute ruin probabilities are given. For the general renewal risk model, we present an asymptotic expression for the infinite-time absolute ruin probability. Conditional distributions of Poisson processes and probabilistic techniques regarding randomly weighted sums are employed in the course of this study.


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