Copula models for insurance claim numbers with excess zeros and time-dependence

Zhao, Xiaobing; Zhou, Xian

doi:10.1016/j.insmatheco.2011.11.004

Cited by 7 publications

(10 citation statements)

References 28 publications

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“…Compared with warranty data, insurance data may contain more information such as information of the policyholders and they are normally panel data [12,13], whereas warranty data are normally not presented as panel data format. Insurance claims occur due to one of the specific perils agreed in the policy whereas warranty claims occur due to product failures.…”

Section: Datamentioning

confidence: 99%

“…However, many researchers find that, in practice, the independence assumption is too restrictive and may not hold. As such, dependence between claims in different periods claimed by a policyholder is considered, based on which many modelling approaches are developed, see [9,[12][13][14][15]40], for example.…”

Section: Dependence Modellingmentioning

confidence: 99%

“…It was first introduced by [53] and has attracted considerable attention in theoretical and application aspects in recent years. In insurance data analysis, copula-based approaches are used to model the dependence between different claim types [10,54], between accident date and reported date [23], between policy coverage and number of claims [17,18,55], between claim counts in successive periods [12,13], between claims in different business lines [56,57], between number 398 of claims and average claim size [4], and between time-to-claim and claim size [8].…”

Section: Dependence In Warranty Data Analysismentioning

confidence: 99%

“…As shown in the above review, insurance data analysis considering random effects has been studied by many authors, see [12,13,15,16,20], for example. In warranty data analysis, the phenomenon of random effects is studied as well.…”

Section: Random Effectsmentioning

confidence: 99%

“…As literature review conducted above, in insurance data analysis, the dependence of the claims frequency of heterogeneous units in successive periods is depicted by the dependence between the random effect variables and modelled by copula [12].…”

Section: Random Effectsmentioning

confidence: 99%

See 4 more Smart Citations

An Overview of Approaches to Insurance Data Analysis and Suggestions for Warranty Data Analysis

Luo¹,

Wu²

2016

ENG

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Warranty shares similarities with insurance in many aspects. Research on insurance data analysis has attracted much more attention than on warranty data analysis. This paper provides a general comparison between warranty and insurance in terms of their coverages, policies and data collection. It then reviews existing approaches to insurance data analysis with regard to modelling of claim frequency, modelling of claim size and policy pricing. Some recent patents relating statistical models are also discussed. The paper concludes with suggestions for improving warranty data analysis.

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Section: Datamentioning

confidence: 99%

Section: Dependence Modellingmentioning

confidence: 99%

Section: Dependence In Warranty Data Analysismentioning

confidence: 99%

Section: Random Effectsmentioning

confidence: 99%

Section: Random Effectsmentioning

confidence: 99%

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An Overview of Approaches to Insurance Data Analysis and Suggestions for Warranty Data Analysis

Luo¹,

Wu²

2016

ENG

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Exponential dispersion models for overdispersed zero-inflated count data

Bar‐Lev

Ridder

2021

Communications in Statistics - Simulation and Computation

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We consider two classes of exponential dispersion models of discrete probability distributions which are defined by specifying their variance functions in their mean value parameterization. These classes were considered in our earlier paper as models of overdispersed zero-inflated distributions. In this paper we analyze the application of these classes to fit count data having overdispersed and zero-inflated statistics. For this reason, we first elaborate on the computational aspects of the probability distributions, before we consider the data fitting with our models. We execute an extensive comparison with other statistical models that are recently proposed, on both real data sets, and simulated data sets. Our findings are that our framework is a flexible tool that gives excellent results in a wide range of cases. Moreover, specifically when the data characteristics show also large skewness and kurtosis our models perform best.

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An Investment and Consumption Problem with CIR Interest Rate and Stochastic Volatility

Chang

Rong

2013

Abstract and Applied Analysis

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We are concerned with an investment and consumption problem with stochastic interest rate and stochastic volatility, in which interest rate dynamic is described by the Cox-Ingersoll-Ross (CIR) model and the volatility of the stock is driven by Heston’s stochastic volatility model. We apply stochastic optimal control theory to obtain the Hamilton-Jacobi-Bellman (HJB) equation for the value function and choose power utility and logarithm utility for our analysis. By using separate variable approach and variable change technique, we obtain the closed-form expressions of the optimal investment and consumption strategy. A numerical example is given to illustrate our results and to analyze the effect of market parameters on the optimal investment and consumption strategies.

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Copula models for insurance claim numbers with excess zeros and time-dependence

Cited by 7 publications

References 28 publications

An Overview of Approaches to Insurance Data Analysis and Suggestions for Warranty Data Analysis

An Overview of Approaches to Insurance Data Analysis and Suggestions for Warranty Data Analysis

Exponential dispersion models for overdispersed zero-inflated count data

An Investment and Consumption Problem with CIR Interest Rate and Stochastic Volatility

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