Ruin probabilities for a risk model with two classes of claims

2010 ◽  
Vol 26 (9) ◽  
pp. 1749-1760 ◽  
Author(s):  
Tong Ling Lv ◽  
Jun Yi Guo ◽  
Xin Zhang
Keyword(s):  
Risk Model ◽  
Ruin Probabilities

Asymptotic ruin probabilities for a bidimensional renewal risk model

Stochastics ◽  
2017 ◽  
Vol 89 (5) ◽  
pp. 687-708 ◽  
Author(s):  
Haizhong Yang ◽  
Jinzhu Li
Keyword(s):  
Risk Model ◽  
Ruin Probabilities ◽  
Renewal Risk Model ◽  
Renewal Risk

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).

scholarly journals Ruin Probabilities in a Finite-Horizon Risk Model with Investment and Reinsurance

2012 ◽  
Vol 49 (04) ◽  
pp. 954-966
Author(s):  
R. Romera ◽  
W. Runggaldier
Keyword(s):  
Financial Market ◽  
Continuous Time ◽  
Ruin Probability ◽  
Risk Model ◽  
Finite Horizon ◽  
Ruin Probabilities ◽  
Optimal Solutions ◽  
Semi Markov Process ◽  
Insurance Model ◽  
Recursive Relations

A finite-horizon insurance model is studied where the risk/reserve process can be controlled by reinsurance and investment in the financial market. Our setting is innovative in the sense that we describe in a unified way the timing of the events, that is, the arrivals of claims and the changes of the prices in the financial market, by means of a continuous-time semi-Markov process which appears to be more realistic than, say, classical diffusion-based models. Obtaining explicit optimal solutions for the minimizing ruin probability is a difficult task. Therefore we derive a specific methodology, based on recursive relations for the ruin probability, to obtain a reinsurance and investment policy that minimizes an exponential bound (Lundberg-type bound) on the ruin probability.

scholarly journals Erlangian Approximations for Finite-Horizon Ruin Probabilities

2002 ◽  
Vol 32 (2) ◽  
pp. 267-281 ◽  
Author(s):  
Soren Asmussen ◽  
Florin Avram ◽  
Miguel Usabel
Keyword(s):  
Ruin Probability ◽  
Risk Model ◽  
Fluid Model ◽  
Ruin Probabilities ◽  
Approximation Procedure ◽  
Exponential Form ◽  
Probability Of Ruin ◽  
Phase Type ◽  
The Matrix ◽  
The Mean

AbstractFor the Cramér-Lundberg risk model with phase-type claims, it is shown that the probability of ruin before an independent phase-type time H coincides with the ruin probability in a certain Markovian fluid model and therefore has an matrix-exponential form. When H is exponential, this yields in particular a probabilistic interpretation of a recent result of Avram & Usabel. When H is Erlang, the matrix algebra takes a simple recursive form, and fixing the mean of H at T and letting the number of stages go to infinity yields a quick approximation procedure for the probability of ruin before time T. Numerical examples are given, including a combination with extrapolation.

scholarly journals Ruin Probabilities in a Dependent Discrete-Time Risk Model With Gamma-Like Tailed Insurance Risks

Risks ◽  
2017 ◽  
Vol 5 (1) ◽  
pp. 14 ◽  
Author(s):  
Xing-Fang Huang ◽  
Ting Zhang ◽  
Yang Yang ◽  
Tao Jiang
Keyword(s):  
Discrete Time ◽  
Risk Model ◽  
Ruin Probabilities

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.

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