Statistical estimation for some dividend problems under the compound Poisson risk model

2020 ◽  
Vol 95 ◽  
pp. 101-115
Author(s):  
Jiayi Xie ◽  
Zhimin Zhang
Keyword(s):  
Statistical Estimation ◽  
Risk Model ◽  
Compound Poisson ◽  
Compound Poisson Risk Model ◽  
Poisson Risk Model

scholarly journals Dynamic Proportional Reinsurance and Approximations for Ruin Probabilities in the Two-Dimensional Compound Poisson Risk Model

2012 ◽  
Vol 2012 ◽  
pp. 1-26 ◽  
Author(s):  
Yan Li ◽  
Guoxin Liu
Keyword(s):  
Ruin Probability ◽  
Risk Model ◽  
Optimal Strategies ◽  
Proportional Reinsurance ◽  
Two Dimensional ◽  
Compound Poisson ◽  
Compound Poisson Risk Model ◽  
Optimal Value ◽  
Hamilton Jacobi Bellman ◽  
Poisson Risk Model

We consider the dynamic proportional reinsurance in a two-dimensional compound Poisson risk model. The optimization in the sense of minimizing the ruin probability which is defined by the sum of subportfolio is being ruined. Via the Hamilton-Jacobi-Bellman approach we find a candidate for the optimal value function and prove the verification theorem. In addition, we obtain the Lundberg bounds and the Cramér-Lundberg approximation for the ruin probability and show that as the capital tends to infinity, the optimal strategies converge to the asymptotically optimal constant strategies. The asymptotic value can be found by maximizing the adjustment coefficient.

scholarly journals Estimates for the Absolute Ruin Probability in the Compound Poisson Risk Model with Credit and Debit Interest

2008 ◽  
Vol 45 (03) ◽  
pp. 818-830 ◽  
Author(s):  
Jinxia Zhu ◽  
Hailiang Yang
Keyword(s):  
Ruin Probability ◽  
Risk Model ◽  
Compound Poisson ◽  
Compound Poisson Risk Model ◽  
Absolute Ruin ◽  
Constant Rate ◽  
Negative Constant ◽  
The Absolute ◽  
Debit Interest ◽  
Poisson Risk Model

In this paper we consider a compound Poisson risk model where the insurer earns credit interest at a constant rate if the surplus is positive and pays out debit interest at another constant rate if the surplus is negative. Absolute ruin occurs at the moment when the surplus first drops below a critical value (a negative constant). We study the asymptotic properties of the absolute ruin probability of this model. First we investigate the asymptotic behavior of the absolute ruin probability when the claim size distribution is light tailed. Then we study the case where the common distribution of claim sizes are heavy tailed.

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