scholarly journals On a Periodic Capital Injection and Barrier Dividend Strategy in the Compound Poisson Risk Model

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 511 ◽  
Author(s):  
Wenguang Yu ◽  
Peng Guo ◽  
Qi Wang ◽  
Guofeng Guan ◽  
Qing Yang ◽  
...  
Keyword(s):  
Risk Model ◽  
Observation Interval ◽  
Claim Amount ◽  
Insurance Company ◽  
Classical Risk Model ◽  
Numerical Examples ◽  
Compound Poisson Risk Model ◽  
Capital Injection ◽  
The Classical Risk Model ◽  
Injection Function

In this paper, we assume that the reserve level of an insurance company can only be observed at discrete time points, then a new risk model is proposed by introducing a periodic capital injection strategy and a barrier dividend strategy into the classical risk model. We derive the equations and the boundary conditions satisfied by the Gerber-Shiu function, the expected discounted capital injection function and the expected discounted dividend function by assuming that the observation interval and claim amount are exponentially distributed, respectively. Numerical examples are also given to further analyze the influence of relevant parameters on the actuarial function of the risk model.

scholarly journals Recursive Calculation of Survival Probabilities

1991 ◽  
Vol 21 (2) ◽  
pp. 199-221 ◽  
Author(s):  
David C. M. Dickson ◽  
Howard R. Waters
Keyword(s):  
Finite Time ◽  
Approximate Calculation ◽  
Risk Model ◽  
Classical Risk Model ◽  
Infinite Time ◽  
Numerical Examples ◽  
Survival Probabilities ◽  
Recursive Calculation ◽  
The Stability ◽  
The Classical Risk Model

AbstractIn this paper we present an algorithm for the approximate calculation of finite time survival probabilities for the classical risk model. We also show how this algorithm can be applied to the calculation of infinite time survival probabilities. Numerical examples are given and the stability of the algorithms is discussed.

scholarly journals Nonparametric Estimation of the Ruin Probability in the Classical Compound Poisson Risk Model

2020 ◽  
Vol 13 (12) ◽  
pp. 298
Author(s):  
Yuan Gao ◽  
Lingju Chen ◽  
Jiancheng Jiang ◽  
Honglong You
Keyword(s):  
Nonparametric Estimation ◽  
Ruin Probability ◽  
Risk Model ◽  
Estimation Method ◽  
Asymptotic Distributions ◽  
Classical Risk Model ◽  
Compound Poisson Risk Model ◽  
The Fourier Transform ◽  
The Classical Risk Model ◽  
Asymptotic Variances

In this paper we study estimating ruin probability which is an important problem in insurance. Our work is developed upon the existing nonparametric estimation method for the ruin probability in the classical risk model, which employs the Fourier transform but requires smoothing on the density of the sizes of claims. We propose a nonparametric estimation approach which does not involve smoothing and thus is free of the bandwidth choice. Compared with the Fourier-transformation-based estimators, our estimators have simpler forms and thus are easier to calculate. We establish asymptotic distributions of our estimators, which allows us to consistently estimate the asymptotic variances of our estimators with the plug-in principle and enables interval estimates of the ruin probability.

scholarly journals On the Expected Discounted Penalty Function for the Classical Risk Model with Potentially Delayed Claims and Random Incomes

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Huiming Zhu ◽  
Ya Huang ◽  
Xiangqun Yang ◽  
Jieming Zhou
Keyword(s):  
Penalty Function ◽  
Risk Model ◽  
Claim Amount ◽  
Classical Risk Model ◽  
Main Claim ◽  
Expected Discounted Penalty Function ◽  
The Laplace Transform ◽  
Discounted Penalty Function ◽  
The Classical Risk Model ◽  
Expected Discounted Penalty

We focus on the expected discounted penalty function of a compound Poisson risk model with random incomes and potentially delayed claims. It is assumed that each main claim will produce a byclaim with a certain probability and the occurrence of the byclaim may be delayed depending on associated main claim amount. In addition, the premium number process is assumed as a Poisson process. We derive the integral equation satisfied by the expected discounted penalty function. Given that the premium size is exponentially distributed, the explicit expression for the Laplace transform of the expected discounted penalty function is derived. Finally, for the exponential claim sizes, we present the explicit formula for the expected discounted penalty function.

scholarly journals On the Ruin Probability Under a Class of Risk Processes

2002 ◽  
Vol 32 (1) ◽  
pp. 81-90 ◽  
Author(s):  
Wang Rongming ◽  
Liu Haifeng
Keyword(s):  
Laplace Transform ◽  
Renewal Process ◽  
Finite Time ◽  
Ruin Probability ◽  
Risk Model ◽  
Claim Amount ◽  
Classical Risk Model ◽  
Finite Time Ruin Probability ◽  
Risk Processes ◽  
The Classical Risk Model

AbstractIn this paper a class of risk processes in which claims occur as a renewal process is studied. A clear expression for Laplace transform of the finite time ruin probability is well given when the claim amount distribution is a mixed exponential. As its consequence, a well-known result about ultimate ruin probability in the classical risk model is obtained.

scholarly journals The Density of the Time to Ruin in the Classical Poisson Risk Model

2005 ◽  
Vol 35 (1) ◽  
pp. 45-60 ◽  
Author(s):  
David C.M. Dickson ◽  
Gordon E. Willmot
Keyword(s):  
Laplace Transform ◽  
Finite Time ◽  
Risk Model ◽  
Erlang Distribution ◽  
Claim Amount ◽  
Ruin Probabilities ◽  
Classical Risk Model ◽  
The Individual ◽  
The Classical Risk Model ◽  
Poisson Risk Model

We derive an expression for the density of the time to ruin in the classical risk model by inverting its Laplace transform. We then apply the result when the individual claim amount distribution is a mixed Erlang distribution, and show how finite time ruin probabilities can be calculated in this case.

scholarly journals The Density of the Time to Ruin in the Classical Poisson Risk Model

2005 ◽  
Vol 35 (01) ◽  
pp. 45-60 ◽  
Author(s):  
David C.M. Dickson ◽  
Gordon E. Willmot
Keyword(s):  
Laplace Transform ◽  
Finite Time ◽  
Risk Model ◽  
Erlang Distribution ◽  
Claim Amount ◽  
Ruin Probabilities ◽  
Classical Risk Model ◽  
The Individual ◽  
The Classical Risk Model ◽  
Poisson Risk Model

We derive an expression for the density of the time to ruin in the classical risk model by inverting its Laplace transform. We then apply the result when the individual claim amount distribution is a mixed Erlang distribution, and show how finite time ruin probabilities can be calculated in this case.

scholarly journals SIMPLE CONTINUITY INEQUALITIES FOR RUIN PROBABILITY IN THE CLASSICAL RISK MODEL

2016 ◽  
Vol 46 (3) ◽  
pp. 801-814 ◽  
Author(s):  
Evgueni Gordienko ◽  
Patricia Vázquez-Ortega
Keyword(s):  
Integral Equations ◽  
Ruin Probability ◽  
Simple Technique ◽  
Risk Model ◽  
Distribution Functions ◽  
Ruin Probabilities ◽  
Classical Risk Model ◽  
Compound Poisson ◽  
Compound Poisson Risk Model ◽  
The Classical Risk Model

AbstractA simple technique for continuity estimation for ruin probability in the compound Poisson risk model is proposed. The approach is based on the contractive properties of operators involved in the integral equations for the ruin probabilities. The corresponding continuity inequalities are expressed in terms of the Kantorovich and weighted Kantorovich distances between distribution functions of claims. Both general and light-tailed distributions are considered.

scholarly journals On Periodic Dividends for the Classical Risk Model with Debit Interest

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Hua Dong ◽  
Xianghua Zhao
Keyword(s):  
Differential Equations ◽  
Risk Model ◽  
Classical Risk Model ◽  
Arrival Times ◽  
Numerical Examples ◽  
Dividend Payments ◽  
Poisson Arrival ◽  
Optimal Dividend ◽  
Debit Interest ◽  
The Classical Risk Model

A periodic dividend problem is studied in this paper. We assume that dividend payments are made at a sequence of Poisson arrival times, and ruin is continuously monitored. First of all, three integro-differential equations for the expected discounted dividends are obtained. Then, we investigate the explicit expressions for the expected discounted dividends, and the optimal dividend barrier is given for exponential claims. A similar study on a generalized Gerber–Shiu function involving the absolute time is also performed. To demonstrate the existing results, we give some numerical examples.

Some Finite Time Ruin Problems

2007 ◽  
Vol 2 (2) ◽  
pp. 217-232 ◽  
Author(s):  
D. C. M. Dickson
Keyword(s):  
Finite Time ◽  
Risk Model ◽  
Claim Amount ◽  
Density Functions ◽  
Classical Risk Model ◽  
Deficit At Ruin ◽  
The Deficit At Ruin ◽  
Aggregate Claims ◽  
The Individual ◽  
The Classical Risk Model

ABSTRACTIn the classical risk model, we use probabilistic arguments to write down expressions in terms of the density function of aggregate claims for joint density functions involving the time to ruin, the deficit at ruin and the surplus prior to ruin. We give some applications of these formulae in the cases when the individual claim amount distribution is exponential and Erlang(2).

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