Notes on discrete compound Poisson model with applications to risk theory

2014 ◽  
Vol 59 ◽  
pp. 325-336 ◽  
Author(s):  
Huiming Zhang ◽  
Yunxiao Liu ◽  
Bo Li
Keyword(s):  
Poisson Model ◽  
Risk Theory ◽  
Compound Poisson ◽  
Compound Poisson Model

scholarly journals Maximizing Dividends without Bankruptcy

2006 ◽  
Vol 36 (01) ◽  
pp. 5-23 ◽  
Author(s):  
Hans U. Gerber ◽  
Elias S.W. Shiu ◽  
Nathaniel Smith
Keyword(s):  
Poisson Model ◽  
Risk Theory ◽  
Claim Amount ◽  
Barrier Strategy ◽  
Deficit At Ruin ◽  
Compound Poisson ◽  
Compound Poisson Model ◽  
The Deficit At Ruin ◽  
The Difference

Consider the classical compound Poisson model of risk theory, in which dividends are paid to the shareholders according to a barrier strategy. Let b* be the level of the barrier that maximizes the expectation of the discounted dividends until ruin. This paper is inspired by Dickson and Waters (2004). They point out that the shareholders should be liable to cover the deficit at ruin. Thus, they consider b0 , the level of the barrier that maximizes the expectation of the difference between the discounted dividends until ruin and the discounted deficit at ruin. In this paper, b* and b0 are compared, when the claim amount distribution is exponential or a combination of exponentials.

scholarly journals Maximizing Dividends without Bankruptcy

2006 ◽  
Vol 36 (1) ◽  
pp. 5-23 ◽  
Author(s):  
Hans U. Gerber ◽  
Elias S.W. Shiu ◽  
Nathaniel Smith
Keyword(s):  
Poisson Model ◽  
Risk Theory ◽  
Claim Amount ◽  
Barrier Strategy ◽  
Deficit At Ruin ◽  
Compound Poisson ◽  
Compound Poisson Model ◽  
The Deficit At Ruin ◽  
The Difference

Consider the classical compound Poisson model of risk theory, in which dividends are paid to the shareholders according to a barrier strategy. Let b* be the level of the barrier that maximizes the expectation of the discounted dividends until ruin. This paper is inspired by Dickson and Waters (2004). They point out that the shareholders should be liable to cover the deficit at ruin. Thus, they consider b0, the level of the barrier that maximizes the expectation of the difference between the discounted dividends until ruin and the discounted deficit at ruin. In this paper, b* and b0 are compared, when the claim amount distribution is exponential or a combination of exponentials.

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 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.

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