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 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.

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 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.

scholarly journals Ruin excursions, the G/G/∞ queue, and tax payments in renewal risk models

2011 ◽  
Vol 48 (A) ◽  
pp. 3-14
Author(s):  
Hansjörg Albrecher ◽  
Sem C. Borst ◽  
Onno J. Boxma ◽  
Jacques Resing
Keyword(s):  
Ruin Probability ◽  
Risk Model ◽  
Risk Models ◽  
Renewal Risk Model ◽  
Insurance Portfolio ◽  
Tax Payments ◽  
Renewal Risk

In this paper we investigate the number and maximum severity of the ruin excursion of the insurance portfolio reserve process in the Cramér–Lundberg model with and without tax payments. We also provide a relation of the Cramér–Lundberg risk model with the G/G/∞ queue and use it to derive some explicit ruin probability formulae. Finally, the renewal risk model with tax is considered, and an asymptotic identity is derived that in some sense extends the tax identity of the Cramér– Lundberg risk model.

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