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 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 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 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.

Finite Time Ruin Probability of the Compound Renewal Model with Constant Interest Rate and Weakly Negatively Dependent Claims with Heavy Tails

2015 ◽  
Vol 17 (01) ◽  
pp. 1540011
Author(s):  
K. K. Thampi
Keyword(s):  
Finite Time ◽  
Ruin Probability ◽  
Heavy Tails ◽  
Risk Model ◽  
Finite Time Ruin Probability ◽  
Interest Force ◽  
Constant Interest Force ◽  
Renewal Risk ◽  
Constant Interest Rate ◽  
Constant Interest

This paper establishes a simple asymptotic formula for the finite time ruin probability of a compound renewal risk model with constant interest force. We assume that the claim sizes are Weakly Negatively Dependent (WND) and identically distributed random variables belonging to the class of regularly varying tails. The results obtained have extended and improved some corresponding results of related papers.

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