scholarly journals Asymptotics for ultimate ruin probability in a by-claim risk model

2021 ◽  
Vol 26 (2) ◽  
pp. 259-270
Author(s):  
Aili Zhang ◽  
Shuang Liu ◽  
Yang Yang
Keyword(s):  
Ruin Probability ◽  
Risk Model ◽  
Asymptotic Formulas ◽  
Dependence Structure ◽  
Simulation Studies ◽  
Main Claim ◽  
Heavy Tailed ◽  
Constant Interest Rate ◽  
Constant Interest ◽  
Theoretical Results

This paper considers a by-claim risk model with constant interest rate in which the main claim and by-claim random vectors form a sequence of independent and identically distributed random pairs with each pair obeying some certain dependence or arbitrary dependence structure. Under the assumption of heavy-tailed claims, we derive some asymptotic formulas for ultimate ruin probability. Some simulation studies are also performed to check the accuracy of the obtained theoretical results via the crude Monte Carlo method.

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.

scholarly journals Approximation for the Finite-Time Ruin Probability of a General Risk Model with Constant Interest Rate and Extended Negatively Dependent Heavy-Tailed Claims

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Yang Yang ◽  
Xin Ma ◽  
Jin-guan Lin
Keyword(s):  
Interest Rate ◽  
Finite Time ◽  
Ruin Probability ◽  
Counting Process ◽  
Risk Model ◽  
Dependence Structure ◽  
Finite Time Ruin Probability ◽  
Heavy Tailed ◽  
Constant Interest Rate ◽  
Constant Interest

We propose a general continuous-time risk model with a constant interest rate. In this model, claims arrive according to an arbitrary counting process, while their sizes have dominantly varying tails and fulfill an extended negative dependence structure. We obtain an asymptotic formula for the finite-time ruin probability, which extends a corresponding result of Wang (2008).

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.

scholarly journals Estimates for the Finite-Time Ruin Probability of a Time-Dependent Risk Model with a Brownian Perturbation

2020 ◽  
Vol 2020 ◽  
pp. 1-5 ◽  
Author(s):  
Kaiyong Wang ◽  
Yongfang Cui ◽  
Yanzhu Mao
Keyword(s):  
Finite Time ◽  
Ruin Probability ◽  
Risk Model ◽  
Time Dependent ◽  
Dependence Structure ◽  
Finite Time Ruin Probability ◽  
Dependent Model ◽  
Heavy Tailed ◽  
Time Dependent Model ◽  
Asymptotic Upper Bound

In this paper, we consider a time-dependent risk model with a Brownian perturbation. In this model, there is a dependence structure between the claim sizes and their corresponding interarrival times. Assuming the claim sizes have subexponential distributions, we obtain the asymptotic lower bound of the finite-time ruin probability. When the claim sizes have distributions from the class L∩D, the asymptotic upper bound of the finite-time ruin probability has been presented. These results confirm that when the claim sizes are heavy-tailed, the asymptotics of the finite-time ruin probability of this time-dependent model are insensitive to the Brownian perturbation.

scholarly journals MARTINGALE METHOD FOR RUIN PROBABILITY IN AN AUTOREGRESSIVE MODEL WITH CONSTANT INTEREST RATE

2003 ◽  
Vol 17 (2) ◽  
pp. 183-198 ◽  
Author(s):  
Hailiang Yang ◽  
Lihong Zhang
Keyword(s):  
Interest Rate ◽  
Autoregressive Model ◽  
Ruin Probability ◽  
Risk Model ◽  
Martingale Method ◽  
Insurance Risk ◽  
Infinite Time ◽  
Probability Of Ruin ◽  
Constant Interest Rate ◽  
Constant Interest

In this article, we consider a discrete-time insurance risk model. An autoregressive model is used to model both the claim process and the premium process. The probability of ruin is examined in a model with a constant interest rate. Both exponential and nonexponential upper bounds are obtained for the ruin probability of an infinite time horizon.

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.

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