scholarly journals On the expected discounted penalty function for the compound Poisson risk model with delayed claims

2011 ◽  
Vol 235 (8) ◽  
pp. 2392-2404 ◽  
Author(s):  
Jie-hua Xie ◽  
Wei Zou
Keyword(s):  
Penalty Function ◽  
Risk Model ◽  
Compound Poisson ◽  
Expected Discounted Penalty Function ◽  
Compound Poisson Risk Model ◽  
Discounted Penalty Function ◽  
Expected Discounted Penalty ◽  
Poisson Risk Model

scholarly journals Estimating the Expected Discounted Penalty Function in a Compound Poisson Insurance Risk Model with Mixed Premium Income

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 305 ◽  
Author(s):  
Yunyun Wang ◽  
Wenguang Yu ◽  
Yujuan Huang ◽  
Xinliang Yu ◽  
Hongli Fan
Keyword(s):  
Penalty Function ◽  
Risk Model ◽  
Insurance Risk ◽  
Compound Poisson ◽  
Expected Discounted Penalty Function ◽  
Fourier Cosine ◽  
Discounted Penalty Function ◽  
Premium Income ◽  
Expected Discounted Penalty ◽  
Insurance Risk Model

In this paper, we consider an insurance risk model with mixed premium income, in which both constant premium income and stochastic premium income are considered. We assume that the stochastic premium income process follows a compound Poisson process and the premium sizes are exponentially distributed. A new method for estimating the expected discounted penalty function by Fourier-cosine series expansion is proposed. We show that the estimation is easily computed, and it has a fast convergence rate. Some numerical examples are also provided to show the good properties of the estimation when the sample size is finite.

scholarly journals A Note on a Generalized Gerber–Shiu Discounted Penalty Function for a Compound Poisson Risk Model

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 891 ◽  
Author(s):  
Jiechang Ruan ◽  
Wenguang Yu ◽  
Ke Song ◽  
Yihan Sun ◽  
Yujuan Huang ◽  
...  
Keyword(s):  
Laplace Transform ◽  
Exponential Distribution ◽  
Penalty Function ◽  
Risk Model ◽  
Recursive Method ◽  
Ruin Time ◽  
Compound Poisson ◽  
Compound Poisson Risk Model ◽  
Discounted Penalty Function ◽  
Poisson Risk Model

In this paper, we propose a new generalized Gerber–Shiu discounted penalty function for a compound Poisson risk model, which can be used to study the moments of the ruin time. First, by taking derivatives with respect to the original Gerber–Shiu discounted penalty function, we construct a relation between the original Gerber–Shiu discounted penalty function and our new generalized Gerber–Shiu discounted penalty function. Next, we use Laplace transform to derive a defective renewal equation for the generalized Gerber–Shiu discounted penalty function, and give a recursive method for solving the equation. Finally, when the claim amounts obey the exponential distribution, we give some explicit expressions for the generalized Gerber–Shiu discounted penalty function. Numerical illustrations are also given to study the effect of the parameters on the generalized Gerber–Shiu discounted penalty function.

The Markov Risk Model under Stochastic Discount Interest Force

2011 ◽  
Vol 179-180 ◽  
pp. 1080-1085
Author(s):  
Yu Juan Huang ◽  
Chun Ming Zhang
Keyword(s):  
Differential Equation ◽  
Penalty Function ◽  
Risk Model ◽  
Standard Wiener Process ◽  
Exponential Distributions ◽  
Expected Discounted Penalty Function ◽  
Geometric Process ◽  
Interest Force ◽  
Discounted Penalty Function ◽  
Expected Discounted Penalty

We investigate the expected discounted penalty function in which the discount interest process is driven by markov process. We obtain the integro-differential equation satisfied by the expected discounted penalty function when interest process is perturbed by standard Wiener process and Poisson-Geometric process. A system of Laplace transforms of the expected discounted penalty function, given the initial environment state, is established from a system of integro-differential equations. One example is given with claim sizes that have exponential distributions.

scholarly journals Perturbed MAP Risk Models with Dividend Barrier Strategies

2009 ◽  
Vol 46 (2) ◽  
pp. 521-541 ◽  
Author(s):  
Eric C. K. Cheung ◽  
David Landriault
Keyword(s):  
Penalty Function ◽  
Risk Model ◽  
Arrival Process ◽  
Risk Models ◽  
Expected Discounted Penalty Function ◽  
Numerical Examples ◽  
Dividend Payments ◽  
Discounted Penalty Function ◽  
Markov Modulated ◽  
Expected Discounted Penalty

In the context of a dividend barrier strategy (see, e.g. Lin, Willmot and Drekic (2003)) we analyze the moments of the discounted dividend payments and the expected discounted penalty function for surplus processes with claims arriving according to a Markovian arrival process (MAP). We show that a relationship similar to the dividend-penalty identity of Gerber, Lin and Yang (2006) can be established for the class of perturbed MAP surplus processes, extending in the process some results of Li and Lu (2008) for the Markov-modulated risk model. Also, we revisit the same ruin-related quantities in an identical MAP risk model with the only exception that the barrier level effective at time t depends on the state of the underlying environment at this time. Similar relationships are investigated and derived. Numerical examples are also considered.

scholarly journals Perturbed MAP Risk Models with Dividend Barrier Strategies

2009 ◽  
Vol 46 (02) ◽  
pp. 521-541 ◽  
Author(s):  
Eric C. K. Cheung ◽  
David Landriault
Keyword(s):  
Penalty Function ◽  
Risk Model ◽  
Arrival Process ◽  
Risk Models ◽  
Expected Discounted Penalty Function ◽  
Numerical Examples ◽  
Dividend Payments ◽  
Discounted Penalty Function ◽  
Markov Modulated ◽  
Expected Discounted Penalty

In the context of a dividend barrier strategy (see, e.g. Lin, Willmot and Drekic (2003)) we analyze the moments of the discounted dividend payments and the expected discounted penalty function for surplus processes with claims arriving according to a Markovian arrival process (MAP). We show that a relationship similar to the dividend-penalty identity of Gerber, Lin and Yang (2006) can be established for the class of perturbed MAP surplus processes, extending in the process some results of Li and Lu (2008) for the Markov-modulated risk model. Also, we revisit the same ruin-related quantities in an identical MAP risk model with the only exception that the barrier level effective at time t depends on the state of the underlying environment at this time. Similar relationships are investigated and derived. Numerical examples are also considered.

The Expected Discounted Penalty Function with Random Income under Stochastic Discount Interest Force

2010 ◽  
Vol 113-116 ◽  
pp. 378-381
Author(s):  
Wen Guang Yu ◽  
Zhi Liu
Keyword(s):  
Poisson Process ◽  
Penalty Function ◽  
Risk Model ◽  
Classical Model ◽  
Expected Discounted Penalty Function ◽  
Renewal Model ◽  
Interest Force ◽  
Discounted Penalty Function ◽  
Premium Income ◽  
Expected Discounted Penalty

We study the delayed risk model with random premium income. The premium process is not a linear function of time in contrast with the classical model, but a Poisson process which is also independent of the claim process. We shall consider the case where the discount interest process is no longer a constant in comparison with the classical expected discounted penalty function, but a stochastic interest driven by Poisson process and Wiener process. The expected discounted penalty function in the delayed renewal model is expressed in terms of the corresponding Gerber-Shiu function in the ordinary renewal model. The obtained results can be viewed as the discrete analogy of the classical Sparre-Anderson risk model.

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