Uniform asymptotics for the compound risk model with dependence structures and constant force of interest

Stochastics ◽  
2021 ◽  
pp. 1-21
Author(s):  
Xijun Liu ◽  
Qingwu Gao
Keyword(s):  
Risk Model ◽  
Constant Force ◽  
Uniform Asymptotics ◽  
Force Of Interest ◽  
Dependence Structures

scholarly journals The probabilities of absolute ruin in the renewal risk model with constant force of interest

2010 ◽  
Vol 47 (2) ◽  
pp. 323-334 ◽  
Author(s):  
Dimitrios G. Konstantinides ◽  
Kai W. Ng ◽  
Qihe Tang
Keyword(s):  
Risk Model ◽  
Asymptotic Expression ◽  
Poisson Model ◽  
Weighted Sums ◽  
Constant Force ◽  
Infinite Time ◽  
Renewal Risk Model ◽  
Absolute Ruin ◽  
Force Of Interest ◽  
Renewal Risk

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.

scholarly journals Numerical Ruin Probability in the Dual Risk Model with Risk-Free Investments

Risks ◽  
2018 ◽  
Vol 6 (4) ◽  
pp. 110 ◽  
Author(s):  
Sooie-Hoe Loke ◽  
Enrique Thomann
Keyword(s):  
Differential Equation ◽  
Integral Equation ◽  
Ruin Probability ◽  
Risk Model ◽  
Constant Force ◽  
Time Of Ruin ◽  
Dual Risk Model ◽  
The Laplace Transform ◽  
Force Of Interest ◽  
The Time Of Ruin

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.

scholarly journals The probabilities of absolute ruin in the renewal risk model with constant force of interest

2010 ◽  
Vol 47 (02) ◽  
pp. 323-334 ◽  
Author(s):  
Dimitrios G. Konstantinides ◽  
Kai W. Ng ◽  
Qihe Tang
Keyword(s):  
Risk Model ◽  
Asymptotic Expression ◽  
Poisson Model ◽  
Weighted Sums ◽  
Constant Force ◽  
Infinite Time ◽  
Renewal Risk Model ◽  
Absolute Ruin ◽  
Force Of Interest ◽  
Renewal Risk

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.

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
Keyword(s):  
Counting Process ◽  
Heavy Tails ◽  
Risk Model ◽  
Tail Probability ◽  
Constant Force ◽  
Insurance Risk ◽  
Asymptotic Results ◽  
Main Claim ◽  
Force Of Interest ◽  
Insurance Risk Model

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.

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