scholarly journals RUIN PROBABILITY UNDER COMPOUND POISSON MODELS WITH RANDOM DISCOUNT FACTOR

2004 ◽  
Vol 18 (1) ◽  
pp. 55-70 ◽  
Author(s):  
Kai W. Ng ◽  
Hailiang Yang ◽  
Lihong Zhang
Keyword(s):  
Ruin Probability ◽  
Risk Model ◽  
Poisson Model ◽  
Convergence Result ◽  
Discount Factor ◽  
Insurance Risk ◽  
Compound Poisson ◽  
Analysis Techniques ◽  
Surplus Process ◽  
Poisson Models

In this article, we consider a compound Poisson insurance risk model with a random discount factor. This model is also known as the compound filtered Poisson model. By using some stochastic analysis techniques, a convergence result for the discounted surplus process, an expression for the ruin probability, and the upper bounds for the ruin probability are obtained.

A Risk Model with Delayed Claims

2013 ◽  
Vol 50 (03) ◽  
pp. 686-702 ◽  
Author(s):  
Angelos Dassios ◽  
Hongbiao Zhao
Keyword(s):  
Asymptotic Formula ◽  
Poisson Process ◽  
Ruin Probability ◽  
Risk Model ◽  
Poisson Model ◽  
Exact Formula ◽  
Poisson Models ◽  
Asymptotic Expressions ◽  
Special Case

In this paper we introduce a simple risk model with delayed claims, an extension of the classical Poisson model. The claims are assumed to arrive according to a Poisson process and claims follow a light-tailed distribution, and each loss payment of the claims will be settled with a random period of delay. We obtain asymptotic expressions for the ruin probability by exploiting a connection to Poisson models that are not time homogeneous. A finer asymptotic formula is obtained for the special case of exponentially delayed claims and an exact formula is obtained when the claims are also exponentially distributed.

scholarly journals A Risk Model with Delayed Claims

2013 ◽  
Vol 50 (3) ◽  
pp. 686-702 ◽  
Author(s):  
Angelos Dassios ◽  
Hongbiao Zhao
Keyword(s):  
Asymptotic Formula ◽  
Poisson Process ◽  
Ruin Probability ◽  
Risk Model ◽  
Poisson Model ◽  
Exact Formula ◽  
Poisson Models ◽  
Asymptotic Expressions ◽  
Special Case

In this paper we introduce a simple risk model with delayed claims, an extension of the classical Poisson model. The claims are assumed to arrive according to a Poisson process and claims follow a light-tailed distribution, and each loss payment of the claims will be settled with a random period of delay. We obtain asymptotic expressions for the ruin probability by exploiting a connection to Poisson models that are not time homogeneous. A finer asymptotic formula is obtained for the special case of exponentially delayed claims and an exact formula is obtained when the claims are also exponentially distributed.

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.

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.

On a Dual Model with Multi-Layer Dividend Strategy under Stochastic Interest

2011 ◽  
Vol 422 ◽  
pp. 775-778
Author(s):  
Jin Sheng Yin
Keyword(s):  
Differential Equations ◽  
Poisson Model ◽  
Dual Model ◽  
Exponential Distributions ◽  
Compound Poisson ◽  
Compound Poisson Model ◽  
Surplus Process ◽  
Stochastic Interest ◽  
Aggregate Claims

In insurance mathematics, a compound Poisson model is often used to describe the aggregate claims of the surplus process. In this paper, we consider the dual model of the compound Poisson model with multi-layer dividend strategy under stochastic interest. We derive a set of integro-differential equations satisfied by the expected total discounted dividends until ruin. The cases where profits follow an exponential distributions are solved.

scholarly journals A Lévy Insurance Risk Process with Tax

2008 ◽  
Vol 45 (02) ◽  
pp. 363-375 ◽  
Author(s):  
Hansjörg Albrecher ◽  
Jean-François Renaud ◽  
Xiaowen Zhou
Keyword(s):  
Ruin Probability ◽  
Risk Model ◽  
Risk Process ◽  
Fluctuation Theory ◽  
Insurance Risk ◽  
Exit Problem ◽  
Tax Payments ◽  
Aggregate Income

Using fluctuation theory, we solve the two-sided exit problem and identify the ruin probability for a general spectrally negative Lévy risk process with tax payments of a loss-carry-forward type. We study arbitrary moments of the discounted total amount of tax payments and determine the surplus level to start taxation which maximises the expected discounted aggregate income for the tax authority in this model. The results considerably generalise those for the Cramér-Lundberg risk model with tax.

scholarly journals The finite-time ruin probability of the compound Poisson model with constant interest force

2005 ◽  
Vol 42 (03) ◽  
pp. 608-619 ◽  
Author(s):  
Qihe Tang
Keyword(s):  
Finite Time ◽  
Ruin Probability ◽  
Poisson Model ◽  
Compound Poisson ◽  
Finite Time Ruin Probability ◽  
Compound Poisson Model ◽  
Interest Force ◽  
Constant Interest Force ◽  
Claim Size Distribution ◽  
Constant Interest

In this paper, we establish a simple asymptotic formula for the finite-time ruin probability of the compound Poisson model with constant interest force and subexponential claims in the case that the initial surplus is large. The formula is consistent with known results for the ultimate ruin probability and, in particular, is uniform for all time horizons when the claim size distribution is regularly varying tailed.

scholarly journals On the Distribution of the Surplus Prior and at Ruin

1999 ◽  
Vol 29 (2) ◽  
pp. 227-244 ◽  
Author(s):  
Hanspeter Schmidli
Keyword(s):  
Asymptotic Behaviour ◽  
Ruin Probability ◽  
Poisson Model ◽  
Subexponential Distributions ◽  
Compound Poisson ◽  
Initial Capital ◽  
Compound Poisson Model ◽  
Explicit Expressions

AbstractConsider a classical compound Poisson model. The safety loading can be positive, negative or zero. Explicit expressions for the distributions of the surplus prior and at ruin are given in terms of the ruin probability. Moreover, the asymptotic behaviour of these distributions as the initial capital tends to infinity are obtained. In particular, for positive safety loading the Cramer case, the case of subexponential distributions and some intermediate cases are discussed.

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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