Compound poisson models in actuarial risk theory

1983 ◽  
Vol 23 (1) ◽  
pp. 63-76 ◽  
Author(s):  
Harry H. Panjer ◽  
Gordon E. Willmot
Keyword(s):  
Risk Theory ◽  
Compound Poisson ◽  
Poisson Models ◽  
Actuarial Risk

scholarly journals Asymptotics of Symmetric Compound Poisson Population Models

2014 ◽  
Vol 24 (1) ◽  
pp. 216-253 ◽  
Author(s):  
THIERRY HUILLET ◽  
MARTIN MÖHLE
Keyword(s):  
Transition Probabilities ◽  
Domain Of Attraction ◽  
Local Limit ◽  
Population Models ◽  
Process Models ◽  
Saddle Point Method ◽  
Regularity Conditions ◽  
Compound Poisson ◽  
Poisson Models ◽  
Simply Generated Trees

Compound Poisson population models are particular conditional branching process models. A formula for the transition probabilities of the backward process for general compound Poisson models is verified. Symmetric compound Poisson models are defined in terms of a parameter θ ∈ (0, ∞) and a power series φ with positive radius r of convergence. It is shown that the asymptotic behaviour of symmetric compound Poisson models is mainly determined by the characteristic value θrφ′(r−). If θrφ′(r−)≥1, then the model is in the domain of attraction of the Kingman coalescent. If θrφ′(r−) < 1, then under mild regularity conditions a condensation phenomenon occurs which forces the model to be in the domain of attraction of a discrete-time Dirac coalescent. The proofs are partly based on the analytic saddle point method. They draw heavily from local limit theorems and from results of S. Janson on simply generated trees, conditioned Galton-Watson trees, random allocations and condensation. Several examples of compound Poisson models are provided and analysed.

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.

COMPOUND POISSON CLAIMS RESERVING MODELS: EXTENSIONS AND INFERENCE

2018 ◽  
Vol 48 (3) ◽  
pp. 1137-1156 ◽  
Author(s):  
Shengwang Meng ◽  
Guangyuan Gao
Keyword(s):  
Linear Models ◽  
Mean Squared Error ◽  
Predictive Distribution ◽  
Compound Poisson ◽  
Poisson Models ◽  
Squared Error ◽  
Run Off ◽  
Mean And Variance ◽  
The Individual ◽  
Over Dispersion

AbstractWe consider compound Poisson claims reserving models applied to the paid claims and to the number of payments run-off triangles. We extend the standard Poisson-gamma assumption to account for over-dispersion in the payment counts and to account for various mean and variance structures in the individual payments. Two generalized linear models are applied consecutively to predict the unpaid claims. A bootstrap is used to estimate the mean squared error of prediction and to simulate the predictive distribution of the unpaid claims. We show that the extended compound Poisson models make reasonable predictions of the unpaid claims.

Practical applications of risk theory. Seminar, 29–30 September 1992

1993 ◽  
Vol 120 (1) ◽  
pp. 211-214
Author(s):  
A. S. Macdonald
Keyword(s):  
Case Studies ◽  
Model Compound ◽  
Risk Model ◽  
Risk Theory ◽  
Risk Models ◽  
Compound Poisson ◽  
Practical Applications ◽  
Collective Risk Model ◽  
Actuarial Mathematics ◽  
Collective Risk

A seminar on ‘The Practical Applications of Risk Theory’ was held at Staple Inn on 29–30 September 1992, organised jointly by the Institute and the Department of Actuarial Mathematics and Statistics at Heriot-Watt University. The aim of the seminar was to combine introductory talks on several aspects of risk theory with detailed presentations of case studies by practitioners.The first three sessions dealt with risk models.Ms Mary Hardy gave a short survey of the classical collective risk model, compound Poisson distributions, and some simple approximations to such distributions.

Moderate- and large-deviation probabilities in actuarial risk theory

1989 ◽  
Vol 21 (04) ◽  
pp. 725-741 ◽  
Author(s):  
Eric Slud ◽  
Craig Hoesman
Keyword(s):  
Strong Approximation ◽  
Large Deviation ◽  
Age Distribution ◽  
Risk Theory ◽  
Renewal Processes ◽  
Collective Risk ◽  
Large Deviation Theorem ◽  
Large Deviation Probabilities ◽  
Actuarial Risk ◽  
Portfolio Size

A general model for the actuarial risk-reserve process as a superposition of compound delayed-renewal processes is introduced and related to previous models which have been used in collective risk theory. It is observed that non-stationarity of the portfolio ‘age-structure' within this model can have a significant impact upon probabilities of ruin. When the portfolio size is constant and the policy age-distribution is stationary, the moderate- and large-deviation probabilities of ruin are bounded and calculated using the strong approximation results of Csörg et al. (1987a, b) and a large-deviation theorem of Groeneboom et al. (1979). One consequence is that for non-Poisson claim-arrivals, the large-deviation probabilities of ruin are noticeably affected by the decision to model many parallel policy lines in place of one line with correspondingly faster claim-arrivals.

Moderate- and large-deviation probabilities in actuarial risk theory

1989 ◽  
Vol 21 (4) ◽  
pp. 725-741 ◽  
Author(s):  
Eric Slud ◽  
Craig Hoesman
Keyword(s):  
Strong Approximation ◽  
Large Deviation ◽  
Age Distribution ◽  
Risk Theory ◽  
Renewal Processes ◽  
Collective Risk ◽  
Large Deviation Theorem ◽  
Large Deviation Probabilities ◽  
Actuarial Risk ◽  
Portfolio Size

A general model for the actuarial risk-reserve process as a superposition of compound delayed-renewal processes is introduced and related to previous models which have been used in collective risk theory. It is observed that non-stationarity of the portfolio ‘age-structure' within this model can have a significant impact upon probabilities of ruin. When the portfolio size is constant and the policy age-distribution is stationary, the moderate- and large-deviation probabilities of ruin are bounded and calculated using the strong approximation results of Csörg et al. (1987a, b) and a large-deviation theorem of Groeneboom et al. (1979). One consequence is that for non-Poisson claim-arrivals, the large-deviation probabilities of ruin are noticeably affected by the decision to model many parallel policy lines in place of one line with correspondingly faster claim-arrivals.

scholarly journals Model Uncertainty in Claims Reserving within Tweedie's Compound Poisson Models

2009 ◽  
Vol 39 (1) ◽  
pp. 1-33 ◽  
Author(s):  
Gareth W. Peters ◽  
Pavel V. Shevchenko ◽  
Mario V. Wüthrich
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Model Uncertainty ◽  
Model Averaging ◽  
Poisson Model ◽  
Compound Poisson ◽  
Poisson Models ◽  
Model Selection Problem

AbstractIn this paper we examine the claims reserving problem using Tweedie's compound Poisson model. We develop the maximum likelihood and Bayesian Markov chain Monte Carlo simulation approaches to fit the model and then compare the estimated models under different scenarios. The key point we demonstrate relates to the comparison of reserving quantities with and without model uncertainty incorporated into the prediction. We consider both the model selection problem and the model averaging solutions for the predicted reserves. As a part of this process we also consider the sub problem of variable selection to obtain a parsimonious representation of the model being fitted.

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