scholarly journals Ruin Probabilities in the Mixed Claim Frequency Risk Models

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Zhao Xiaoqin ◽  
Chuangxia Huang
Keyword(s):  
Probability Theory ◽  
Ruin Probabilities ◽  
Risk Models ◽  
Martingale Approach ◽  
Claim Frequency

We consider two mixed claim frequency risk models. Some important probabilistic properties are obtained by probability-theory methods. Some important results about ruin probabilities are obtained by martingale approach.

scholarly journals Discrete-Time Risk Models with Claim Correlated Premiums in a Markovian Environment

Risks ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 26
Author(s):  
Dhiti Osatakul ◽  
Xueyuan Wu
Keyword(s):  
Discrete Time ◽  
Risk Model ◽  
Insurance Industry ◽  
External Environment ◽  
Ruin Probabilities ◽  
Risk Models ◽  
Markovian Environment ◽  
Life Insurance Industry ◽  
Claim Frequency ◽  
The Impact

In this paper we consider a discrete-time risk model, which allows the premium to be adjusted according to claims experience. This model is inspired by the well-known bonus-malus system in the non-life insurance industry. Two strategies of adjusting periodic premiums are considered: aggregate claims or claim frequency. Recursive formulae are derived to compute the finite-time ruin probabilities, and Lundberg-type upper bounds are also derived to evaluate the ultimate-time ruin probabilities. In addition, we extend the risk model by considering an external Markovian environment in which the claims distributions are governed by an external Markov process so that the periodic premium adjustments vary when the external environment state changes. We then study the joint distribution of premium level and environment state at ruin given ruin occurs. Two numerical examples are provided at the end of this paper to illustrate the impact of the initial external environment state, the initial premium level and the initial surplus on the ruin probability.

scholarly journals On a Class of Semi-Markov Risk Models Obtained as Classical Risk Models in a Markovian Environment

1984 ◽  
Vol 14 (1) ◽  
pp. 23-43 ◽  
Author(s):  
Jean-Marie Reinhard
Keyword(s):  
Risk Model ◽  
Risk Process ◽  
Ruin Probabilities ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Risk Models ◽  
Markovian Environment ◽  
Necessary And Sufficient ◽  
Natural Way ◽  
Quantities Of Interest

AbstractWe consider a risk model in which the claim inter-arrivals and amounts depend on a markovian environment process. Semi-Markov risk models are so introduced in a quite natural way. We derive some quantities of interest for the risk process and obtain a necessary and sufficient condition for the fairness of the risk (positive asymptotic non-ruin probabilities). These probabilities are explicitly calculated in a particular case (two possible states for the environment, exponential claim amounts distributions).

COLLECTIVE RISK MODELS WITH DEPENDENCE UNCERTAINTY

2017 ◽  
Vol 47 (2) ◽  
pp. 361-389 ◽  
Author(s):  
Haiyan Liu ◽  
Ruodu Wang
Keyword(s):  
Value At Risk ◽  
Random Variable ◽  
Actuarial Science ◽  
Risk Models ◽  
Worst Case ◽  
Collective Risk ◽  
Approximation Errors ◽  
Claim Frequency ◽  
Aggregate Loss ◽  
The Individual

AbstractWe bring the recently developed framework of dependence uncertainty into collective risk models, one of the most classic models in actuarial science. We study the worst-case values of the Value-at-Risk (VaR) and the Expected Shortfall (ES) of the aggregate loss in collective risk models, under two settings of dependence uncertainty: (i) the counting random variable (claim frequency) and the individual losses (claim sizes) are independent, and the dependence of the individual losses is unknown; (ii) the dependence of the counting random variable and the individual losses is unknown. Analytical results for the worst-case values of ES are obtained. For the loss from a large portfolio of insurance policies, an asymptotic equivalence of VaR and ES is established. Our results can be used to provide approximations for VaR and ES in collective risk models with unknown dependence. Approximation errors are obtained in both cases.

Tail equivalence relationships for ruin probabilities in several risk models

2005 ◽  
Vol 21 (6) ◽  
pp. 499-508 ◽  
Author(s):  
Feng Hu ◽  
Chuancun Yin ◽  
Zhaojun Zong
Keyword(s):  
Ruin Probabilities ◽  
Risk Models

scholarly journals Exponential bounds of ruin probabilities for non-homogeneous risk models

2020 ◽  
Vol 41 (2) ◽  
Author(s):  
Qianqian Zhou ◽  
Alexander Sakhanenko ◽  
Junyi Guo
Keyword(s):  
Ruin Probabilities ◽  
Risk Models ◽  
Exponential Bounds
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