scholarly journals Parisian ruin probability for two-dimensional Brownian risk model

2021 ◽  
pp. 109327
Author(s):  
Konrad Krystecki
Keyword(s):  
Ruin Probability ◽  
Risk Model ◽  
Two Dimensional ◽  
Parisian Ruin

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.

Simultaneous ruin probability for two-dimensional brownian risk model

2020 ◽  
Vol 57 (2) ◽  
pp. 597-612 ◽  
Author(s):  
Krzysztof Dȩbicki ◽  
Enkelejd Hashorva ◽  
Zbigniew Michna
Keyword(s):  
Ruin Probability ◽  
Time Horizon ◽  
Asymptotic Theory ◽  
Risk Model ◽  
Two Dimensional ◽  
Infinite Time ◽  
Ruin Time ◽  
Initial Capital ◽  
Infinite Time Horizon

AbstractThe ruin probability in the classical Brownian risk model can be explicitly calculated for both finite and infinite time horizon. This is not the case for the simultaneous ruin probability in the two-dimensional Brownian risk model. Relying on asymptotic theory, we derive in this contribution approximations for both simultaneous ruin probability and simultaneous ruin time for the two-dimensional Brownian risk model when the initial capital increases to infinity.

On the Parisian ruin of the dual Lévy risk model

2017 ◽  
Vol 54 (4) ◽  
pp. 1193-1212 ◽  
Author(s):  
Chen Yang ◽  
Kristian P. Sendova ◽  
Zhong Li
Keyword(s):  
Ruin Probability ◽  
Risk Model ◽  
Drift Diffusion Model ◽  
Drift Diffusion ◽  
Expected Discounted Penalty Function ◽  
Numerical Examples ◽  
Discounted Penalty Function ◽  
Usual Concept ◽  
Parisian Ruin ◽  
Expected Discounted Penalty

AbstractIn this paper we investigate the Parisian ruin problem of the general dual Lévy risk model. Unlike the usual concept of ultimate ruin, allowing the surplus level to be negative within a prespecified period indicates that the deficit at Parisian ruin is not necessarily equal to zero. Hence, we consider a Gerber–Shiu type expected discounted penalty function at the Parisian ruin and obtain an explicit expression for this function under the dual Lévy risk model. As particular cases, we calculate the Parisian ruin probability and the expected discountedkth moments of the deficit at the Parisian ruin for the compound Poisson dual risk model and a drift-diffusion model. Numerical examples are given to illustrate the behavior of Parisian ruin and the expected discounted deficit at Parisian ruin.

scholarly journals Estimating Ruin Probability in an Insurance Risk Model with Stochastic Premium Income Based on the CFS Method

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 982
Author(s):  
Yujuan Huang ◽  
Jing Li ◽  
Hengyu Liu ◽  
Wenguang Yu
Keyword(s):  
Fourier Series ◽  
Ruin Probability ◽  
Risk Model ◽  
Expansion Method ◽  
Nonparametric Estimator ◽  
Insurance Risk ◽  
Numerical Examples ◽  
Complex Fourier Series ◽  
Premium Income ◽  
Insurance Risk Model

This paper considers the estimation of ruin probability in an insurance risk model with stochastic premium income. We first show that the ruin probability can be approximated by the complex Fourier series (CFS) expansion method. Then, we construct a nonparametric estimator of the ruin probability and analyze its convergence. Numerical examples are also provided to show the efficiency of our method when the sample size is finite.

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