73 research outputs found

    Building Loss Models

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    This paper is intended as a guide to building insurance risk (loss) models. A typical model for insurance risk, the so-called collective risk model, treats the aggregate loss as having a compound distribution with two main components: one characterizing the arrival of claims and another describing the severity (or size) of loss resulting from the occurrence of a claim. In this paper we first present efficient simulation algorithms for several classes of claim arrival processes. Then we review a collection of loss distributions and present methods that can be used to assess the goodness-of-fit of the claim size distribution. The collective risk model is often used in health insurance and in general insurance, whenever the main risk components are the number of insurance claims and the amount of the claims. It can also be used for modeling other non-insurance product risks, such as credit and operational risk.Insurance risk model; Loss distribution; Claim arrival process; Poisson process; Renewal process; Random variable generation; Goodness-of-fit testing

    Building Loss Models

    Get PDF
    This paper is intended as a guide to building insurance risk (loss) models. A typical model for insurance risk, the so-called collective risk model, treats the aggregate loss as having a compound distribution with two main components: one characterizing the arrival of claims and another describing the severity (or size) of loss resulting from the occurrence of a claim. In this paper we first present efficient simulation algorithms for several classes of claim arrival processes. Then we review a collection of loss distributions and present methods that can be used to assess the goodness-of-fit of the claim size distribution. The collective risk model is often used in health insurance and in general insurance, whenever the main risk components are the number of insurance claims and the amount of the claims. It can also be used for modeling other non-insurance product risks, such as credit and operational risk.Insurance risk model; Loss distribution; Claim arrival process; Poisson process; Renewal process; Random variable generation; Goodness-of-fit testing;

    Heterogeneity Pursuit for Spatial Point Pattern with Application to Tree Locations: A Bayesian Semiparametric Recourse

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    Spatial point pattern data are routinely encountered. A flexible regression model for the underlying intensity is essential to characterizing the spatial point pattern and understanding the impacts of potential risk factors on such pattern. We propose a Bayesian semiparametric regression model where the observed spatial points follow a spatial Poisson process with an intensity function which adjusts a nonparametric baseline intensity with multiplicative covariate effects. The baseline intensity is piecewise constant, approached with a powered Chinese restaurant process prior which prevents an unnecessarily large number of pieces. The parametric regression part allows for variable selection through the spike-slab prior on the regression coefficients. An efficient Markov chain Monte Carlo (MCMC) algorithm is developed for the proposed methods. The performance of the methods is validated in an extensive simulation study. In application to the locations of Beilschmiedia pendula trees in the Barro Colorado Island forest dynamics research plot in central Panama, the spatial heterogeneity is attributed to a subset of soil measurements in addition to geographic measurements with a spatially varying baseline intensity.Comment: 21 pages, 7 figure

    Smooth flexible models of nonhomogeneous Poisson processes fit to one or more process realizations

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    Simulation is a technique of creating representations or models of real world systems or processes and conducting experiments to predict behavior of actual systems. Input modeling is a critical aspect of simulation modeling. Stochastic input models are used to model various aspects of the system under uncertainty including process times and interarrival times. This research focuses on input models for nonstationary arrival processes that can be represented as nonhomogeneous Poisson processes (NHPPs). In particular, a smooth flexible model for the mean-value function (or integrated rate function) of a general NHPP is estimated. To represent the mean-value function, the method utilizes a specially formulated polynomial that is constrained in least-squares estimation to be nondecreasing so the corresponding rate function is nonnegative and continuously differentiable. The degree of the polynomial is determined by applying a modified likelihood ratio test to a set of transformed arrival times resulting from a variance stabilizing transformation of the observed data. Given the degree of polynomial, final estimates of the polynomial coefficients are obtained from original arrival times using least-squares estimation. The method is extended to fit an NHPP model to multiple observed realizations of a process. In addition, the method is adapted to a multiresolution procedure that effectively models NHPPs with long term trend and cyclic behavior given multiple process realizations. An experimental performance evaluation is conducted to determine the capabilities and limitations of the NHPP fitting procedure for single and multiple realizations of test processes. The method is implemented in a Java-based programming environment along with a web interface that allows user to upload observed data, fit an NHPP, and generate realizations of the fitted NHPP for use in simulation experiments

    Quantifying and reducing Input modelling error in simulation

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    This thesis presents new methodology in the field of quantifying and reducing input modelling error in computer simulation. Input modelling error is the uncertainty in the output of a simulation that propagates from the errors in the input models used to drive it. When the input models are estimated from observations of the real-world system input modelling error will always arise as only a finite number of observations can ever be collected. Input modelling error can be broken down into two components: variance, known in the literature as input uncertainty; and bias. In this thesis new methodology is contributed for the quantification of both of these sources of error. To date research into input modelling error has been focused on quantifying the input uncertainty (IU) variance. In this thesis current IU quantification techniques for simulation models with time homogeneous inputs are extended to simulation models with nonstationary input processes. Unlike the IU variance, the bias caused by input modelling has, until now, been virtually ignored. This thesis provides the first method for quantifying bias caused by input modelling. Also presented is a bias detection test for identifying, with controlled power, a bias due to input modelling of a size that would be concerning to a practitioner. The final contribution of this thesis is a spline-based arrival process model. By utilising a highly flexible spline representation, the error in the input model is reduced; it is believed that this will also reduce the input modelling error that passes to the simulation output. The methods described in this thesis are not available in the current literature and can be used in a wide range of simulation contexts for quantifying input modelling error and modelling input processes

    Building Loss Models

    Get PDF
    This paper is intended as a guide to building insurance risk (loss) models. A typical model for insurance risk, the so-called collective risk model, treats the aggregate loss as having a compound distribution with two main components: one characterizing the arrival of claims and another describing the severity (or size) of loss resulting from the occurrence of a claim. In this paper we first present efficient simulation algorithms for several classes of claim arrival processes. Then we review a collection of loss distributions and present methods that can be used to assess the goodness-of-fit of the claim size distribution. The collective risk model is often used in health insurance and in general insurance, whenever the main risk components are the number of insurance claims and the amount of the claims. It can also be used for modeling other non-insurance product risks, such as credit and operational risk

    A general-purpose tool for reliability and availability analysis of repairable systems

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    Mestrado de dupla diplomação com a UTFPR - Universidade Tecnológica Federal do ParanáThis thesis covers general mathematical and simulation models for the reliability and availability analysis of repairable systems along with estimation methods and model selection criterion. A combined mathematical and simulation model called the Failure-Repair Process is proposed, based on the trend-renewal process. This model is based on a binary state system, where the system may only be in one of two states: working or failed. This model is then integrated into a general-purpose tool, for automated modelling of repairable systems. The classical Akaike information criterion is used to automate the choice of failure and repair models that best fit the available data. Estimators for different performance measures of the systems are studied, such as point and mean availability, rate of occurrence of failures and a first order reliability estimator based on the Kaplan-Meier estimator. Numerical studies are conducted in the proposed non-analytical estimators for the availability, leading to a robust mean availability estimator and a intuitive but sample demanding point availability estimator. Furthermore, a complete quantitative study is conducted on real data from the food industry together with a presentation of the implemented tool functionalities. Overall, the proposed model is able to adapt very well to real data with different characteristics, and, consequently, the resulting performance indicators are befitting to practice.Esta tese aborda modelos matemáticos e de simulação para a análise de confiabilidade e disponibilidade de sistemas reparáveis, juntamente com métodos de estimação e critério de seleção de modelos. Um modelo matemático e de simulação combinados denominado Failure-Repair Process é proposto, baseado no trend-renewal process. Este modelo consiste em um sistema de caracterização binária, onde o sistema pode estar em apenas um de dois estados: em funcionamento ou falha. Este modelo é então integrado em uma ferramenta de uso geral, para modelagem automatizada de sistemas reparáveis. O clássico critério de informação de Akaike é usado para automatizar a escolha dos modelos de falha e reparo que melhor se ajustam aos dados disponíveis. São estudados estimadores para diferentes medidas de desempenho dos sistemas, tais como disponibilidade pontual e média, taxa de ocorrência de falhas e um estimador de confiabilidade de primeira ordem baseado no estimador Kaplan-Meier. Estudos numéricos são conduzidos nos estimadores nãoanalíticos propostos para a disponibilidade, levando a um estimador de disponibilidade média robusto e um estimador de disponibilidade puntual intuitivo, mas que demanda grandes amostras. Além disso, é realizado um estudo quantitativo completo sobre dados reais da indústria de alimentos juntamente com uma apresentação das funcionalidades da ferramenta implementada. De maneira geral, o modelo proposto é capaz de se adaptar muito bem a dados reais com diferentes características e, consequentemente, os indicadores de desempenho resultantes são adequados à prática
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