scholarly journals A PARTICULAR BIDIMENSIONAL TIME-DEPENDENT RENEWAL RISK MODEL WITH CONSTANT INTEREST RATES

2019 ◽  
Vol 34 (2) ◽  
pp. 172-182
Author(s):  
Ke-Ang Fu ◽  
Chang Ni ◽  
Hao Chen
Keyword(s):  
Interest Rates ◽  
Risk Model ◽  
Asymptotic Expression ◽  
Insurance Companies ◽  
Dependence Structure ◽  
Arrival Times ◽  
Aggregate Claims ◽  
Renewal Risk ◽  
Premium Income ◽  
Constant Interest

AbstractConsider a particular bidimensional risk model, in which two insurance companies divide between them in different proportions both the premium income and the aggregate claims. In practice, it can be interpreted as an insurer–reinsurer scenario, where the reinsurer takes over a proportion of the insurer's losses. Under the assumption that the claim sizes and inter-arrival times form a sequence of independent and identically distributed random pairs, with each pair obeying a dependence structure, an asymptotic expression for the ruin probability of this bidimensional risk model with constant interest rates is established.

Precise Large Deviation of Claim Surplus Process in a Renewal Risk Model with Random Premium Income

2013 ◽  
Vol 850-851 ◽  
pp. 771-775
Author(s):  
Ying Hua Dong
Keyword(s):  
Risk Model ◽  
Large Deviation ◽  
Compound Poisson Process ◽  
Dependence Structure ◽  
Arrival Times ◽  
Renewal Risk Model ◽  
Surplus Process ◽  
Precise Large Deviation ◽  
Renewal Risk ◽  
Premium Income

In this paper, we consider a nonstandard renewal risk model in which claim sizes and corresponding inter-arrival times form a sequence of independent and identically distributed random pairs. Each pair satisfies a certain dependence structure. In addition, premium income is described by a compound Poisson process. When the distribution of claim sizes belongs to the consistent variation class, we obtain precise large deviation of claim surplus process.

Subexponential tails of discounted aggregate claims in a time-dependent renewal risk model

2010 ◽  
Vol 42 (4) ◽  
pp. 1126-1146 ◽  
Author(s):  
Jinzhu Li ◽  
Qihe Tang ◽  
Rong Wu
Keyword(s):  
Asymptotic Formula ◽  
Risk Model ◽  
Tail Probability ◽  
Dependence Structure ◽  
Claim Size ◽  
Claim Size Distribution ◽  
Discounted Aggregate Claims ◽  
Aggregate Claims ◽  
Renewal Risk ◽  
The Impact

Consider a continuous-time renewal risk model with a constant force of interest. We assume that claim sizes and interarrival times correspondingly form a sequence of independent and identically distributed random pairs and that each pair obeys a dependence structure described via the conditional tail probability of a claim size given the interarrival time before the claim. We focus on determining the impact of this dependence structure on the asymptotic tail probability of discounted aggregate claims. Assuming that the claim size distribution is subexponential, we derive an exact locally uniform asymptotic formula, which quantitatively captures the impact of the dependence structure. When the claim size distribution is extended regularly varying tailed, we show that this asymptotic formula is globally uniform.

scholarly journals Asymptotic Ruin Probability of a Bidimensional Risk Model Based on Entrance Processes with Constant Interest Rate

Risks ◽  
2018 ◽  
Vol 6 (4) ◽  
pp. 135
Author(s):  
Hongmin Xiao ◽  
Lin Xie
Keyword(s):  
Ruin Probability ◽  
Risk Model ◽  
Dependence Structure ◽  
Arrival Times ◽  
Interest Force ◽  
Heavy Tailed Distribution ◽  
Constant Interest Force ◽  
Heavy Tailed ◽  
Constant Interest Rate ◽  
Constant Interest

In this paper, the risk model with constant interest based on an entrance process is investigated. Under the assumptions that the entrance process is a renewal process and the claims sizes satisfy a certain dependence structure, which belong to the different heavy-tailed distribution classes, the finite-time asymptotic estimate of the bidimensional risk model with constant interest force is obtained. Particularly, when inter-arrival times also satisfy a certain dependence structure, these formulas still hold.

Subexponential tails of discounted aggregate claims in a time-dependent renewal risk model

2010 ◽  
Vol 42 (04) ◽  
pp. 1126-1146 ◽  
Author(s):  
Jinzhu Li ◽  
Qihe Tang ◽  
Rong Wu
Keyword(s):  
Asymptotic Formula ◽  
Risk Model ◽  
Tail Probability ◽  
Dependence Structure ◽  
Claim Size ◽  
Claim Size Distribution ◽  
Discounted Aggregate Claims ◽  
Aggregate Claims ◽  
Renewal Risk ◽  
The Impact

Consider a continuous-time renewal risk model with a constant force of interest. We assume that claim sizes and interarrival times correspondingly form a sequence of independent and identically distributed random pairs and that each pair obeys a dependence structure described via the conditional tail probability of a claim size given the interarrival time before the claim. We focus on determining the impact of this dependence structure on the asymptotic tail probability of discounted aggregate claims. Assuming that the claim size distribution is subexponential, we derive an exact locally uniform asymptotic formula, which quantitatively captures the impact of the dependence structure. When the claim size distribution is extended regularly varying tailed, we show that this asymptotic formula is globally uniform.

scholarly journals Ruin Problems of Multidimensional Risk Models under Constant Interest Rates and Dependent Risks with Heavy Tails

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Xinmei Shen ◽  
Meng Yuan ◽  
Dawei Lu
Keyword(s):  
Interest Rates ◽  
Ruin Probability ◽  
Heavy Tails ◽  
Optimal Allocation ◽  
Risk Model ◽  
Dependence Structure ◽  
Asymptotic Estimates ◽  
Risk Models ◽  
Dependent Risks ◽  
Constant Interest

Consider a discrete-time multidimensional risk model with constant interest rates where capital transfers between lines are partially allowed over each period. By assuming a large initial capital and regularly varying distributions for the losses, we derive asymptotic estimates for the ruin probability under some dependence structure and study the optimal allocation of the initial reserve. Some numerical simulations are provided to illuminate our main results.

scholarly journals Precise large deviations for the aggregate claims in a dependent compound renewal risk model

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Kaiyong Wang ◽  
Lamei Chen
Keyword(s):  
Large Deviations ◽  
Risk Model ◽  
Tail Probability ◽  
Dependence Structure ◽  
Precise Large Deviations ◽  
Renewal Risk Model ◽  
Aggregate Claims ◽  
Renewal Risk ◽  
Distribution Class ◽  
Compound Renewal Risk Model

Abstract We consider a dependent compound renewal risk model, where the interarrival times of accidents and the claim numbers follow a dependence structure characterized by a conditional tail probability and the claim sizes have a pairwise negatively quadrant dependence structure or a related dependence structure with the upper tail asymptotical dependence structure. When the distributions of the claim sizes belong to the dominated variation distribution class, we give the asymptotic lower and upper bounds for the precise large deviations of the aggregate claims.

scholarly journals The Asymptotics of Recovery Probability in the Dual Renewal Risk Model with Constant Interest and Debit Force

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Hao Wang ◽  
Lin Xu
Keyword(s):  
Asymptotic Behavior ◽  
Discrete Time ◽  
Risk Model ◽  
Continuous Time Model ◽  
Time Model ◽  
Discrete Time Model ◽  
Renewal Risk Model ◽  
Renewal Risk ◽  
Premium Income ◽  
Constant Interest

The asymptotic behavior of the recovery probability for the dual renewal risk model with constant interest and debit force is studied. By means the idea of Markov Skeleton method, we studied the times that the random premium incomes happened and transformed the continuous time model into a discrete time model. By investigating the fluctuations of this discrete time model, we obtained the asymptotic behavior when the random premium income belongs to a kind of heavy-tailed distributions.

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.

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