Insurance Applications of Some New Dependence Models Derived from Multivariate Collective Models PDF Download

Author: Enkelejd Hashorva
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Languages : en
Pages : 21

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Consider two different portfolios which have claims triggered by the same events. Their corresponding collective model over a fixed time period is given in terms of individual claim sizes $(X_i,Y_i), i ge 1$ and a claim counting random variable $N$. In this paper we are concerned with the joint distribution function $F$ of the largest claim sizes $(X_{N:N}, Y_{N:N})$. By allowing $N$ to depend on some parameter, say $ theta$, then $F=F( theta)$ is for various choices of $N$ a tractable parametric family of bivariate distribution functions. We present three applications of the implied parametric models to some data from the literature and a new data set from a Swiss insurance company. Furthermore, we investigate both distributional and asymptotic properties of $(X_{N:N,Y_{N:N})$

Author: Junjie Liu
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Category : Copulas (Mathematical statistics)
Languages : en
Pages : 0

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Random effects models are of particular importance in modeling heterogeneity. A commonly used random effects model for multivariate survival analysis is the frailty model. In this thesis, a special frailty model with an Archimedean dependence structure is used to model dependent risks. This modeling approach allows the construction of multivariate distributions through a copula with univariate marginal distributions as parameters. Copulas are constructed by modeling distribution functions and survival functions, respectively. Measures of the dependence are applied for the copula model selections. Tail-based risk measures for the functions of two dependent variables are investigated for particular interest. The statistical application of the copula modeling approach to an insurance data set is discussed where losses and loss adjustment expenses data are used. Insurance applications based on the fitted model are illustrated.

Author: Gee Yul Lee
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Languages : en
Pages : 0

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This dissertation contributes to the risk and insurance literature by expanding our understanding of insurance claims modeling, deductible ratemaking, and the insurance risk retention problem. In the claims modeling part, a data-driven approach is taken to analyze insurance losses using statistical methods. It is often common for an analyst to be interested in several outcome measures depending on a large set of explanatory variables, with the goal of understanding both the average behavior, and the overall distribution of the outcomes. The use of multivariate analysis has an advantage in a broad context, and the literature on multivariate regression modeling is extended with a focus on dependence among multiple insurance lines. In this process, a deductible is an important feature of an insurance policy to consider, because it may influence the frequency and severity of claims to be censored or truncated. Standard textbooks have approached deductible ratemaking using models for coverage modification, utilizing parametric loss distributions. In practice, regression could be used with explanatory variables including the deductible amount. The various approaches to deductible ratemaking are compared in this dissertation. Ultimately, an insurance manager would be interested in understanding the influence of a retention parameter change to the risk of a portfolio of losses. The retention parameter may be deductible, upper limit, or coinsurance. This dissertation contributes to the statistics and actuarial literature by introducing and applying the 01-inflated negative binomial frequency model (a frequency model for observations with an inflated number of zeros and ones), and illustrating how discrete and continuous copula methods can be empirically applied to insurance claims analysis. In the process, the dissertation provides a comparison among various deductible analysis procedures, and shows that the regression approach has an advantage in problems of moderate size. Finally, the dissertation attempts to broaden our understanding of the risk retention problem within a constrained optimization framework, and demonstrates the quasiconvexity of the objective function in this problem. The dissertation reveals that the loading factor of a reinsurance premium has a risk measure interpretation, and relates to the risk measure relative margins (RMRM). Concepts are illustrated using the Wisconsin Local Government Property Insurance Fund (LGPIF) data.

Author: Marie-Pier Côté
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Category :
Languages : en
Pages :

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"Modeling the dependence between risks is crucial for the computation of the economic capital and the variability of insurance liabilities. It is thus not surprising that copula (regression) models are widely used in actuarial applications. In this thesis, three topics on dependence modeling for insurance risks are considered. The first part of this work explores the probabilistic features of the dependence structures underlying the background risk model (RX, RY), where R is a strictly positive random variable independent of the random vector (X,Y). This broad class of copulas encompasses Archimedean and elliptical copulas, but also new interesting models, some of which yield explicit expressions for the distribution and tail-value-at-risk of the sum RX+RY. The remainder of the thesis is more statistical in nature. There are numerous actuarial applications of copula models where marginal distributions vary with covariates, but few tools are available for inference in that context. In the second part of the thesis, the validity of rank-based tools for copula inference is established under carefully designed assumptions that hold for all the covariate dependent marginal distributions commonly used for modeling insurance data. Simulation studies are performed in two property and casualty insurance examples: loss triangles for two lines of business and micro-level multivariate claim amounts. The latter example is treated in details in a Bayesian data analysis reported in the last part of this thesis. The model accounts for the dependence between claimants involved in a single event and between amounts paid to a claimant under different insurance coverages. A multiple imputation procedure allows to include the information contained in open claimant files, without which the inference is biased towards simple claims." --

Author: Marco Bee
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Category :
Languages : en
Pages : 27

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The purpose of this paper consists in analysing the relevance of dependence concepts in finance, insurance and risk management, exploring how these concepts can be implemented in a statistical model via copula functions and pointing out some difficulties related to this methodology. In particular, we first review the statistical models currently used in the actuarial and financial fields when dealing with loss data; then we show, by means of two risk management applications, that copula-based models are very flexible but sometimes difficult to set up and to estimate; finally we study, by means of a simulation experiment, the properties of the maximum likelihood estimators of the Gaussian and Gumbel copula.

Author: Hélène Cossette
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Category :
Languages : en
Pages : 31

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In actuarial science, collective risk models, in which the aggregate claim amount of a portfolio is defined in terms of random sums, play a crucial role. In these models, it is common to assume that the number of claims and their amounts are independent, even if this might not always be the case. We consider collective risk models with different dependence structures. Due to the importance of such distributions in an actuarial setting, we first investigate a collective risk model with dependence involving the family of multivariate mixed Erlang distributions. Other models based on mixtures involving bivariate and multivariate copulas in a more general setting are then presented. These different structures allow to link the number of claims to each claim amount, and to quantify the aggregate claim loss. Then, we use Archimedean and hierarchical Archimedean copulas in collective risk models, to model the dependence between the claim number random variable and the claim amount random variables involved in the random sum. Such dependence structures allow us to derive a computational methodology for the assessment of the aggregate claim amount. While being very flexible, this methodology is easy to implement, and can easily fit more complicated hierarchical structures.

Author: Wei Wei
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ISBN:
Category :
Languages : en
Pages : 162

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Book Description
Many insurance and finance activities involve multiple risks. Dependence structures between different risks play an important role in both theoretical models and practical applications. However, stochastic and actuarial models with dependence are very challenging research topics. In most literature, only special dependence structures have been considered. However, most existing special dependence structures can be integrated into more-general contexts. This thesis is motivated by the desire to develop more-general dependence structures and to consider their applications. This thesis systematically studies different dependence notions and explores their applications in the fields of insurance and finance. It contributes to the current literature in the following three main respects. First, it introduces some dependence notions to actuarial science and initiates a new approach to studying optimal reinsurance problems. Second, it proposes new notions of dependence and provides a general context for the studies of optimal allocation problems in insurance and finance. Third, it builds the connections between copulas and the proposed dependence notions, thus enabling the constructions of the proposed dependence structures and enhancing their applicability in practice. The results derived in the thesis not only unify and generalize the existing studies of optimization problems in insurance and finance, but also admit promising applications in other fields, such as operations research and risk management.

Author: Himchan Jeong
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Languages : en
Pages : 0

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In the ratemaking for general insurance, calculation of the pure premium has traditionally been based on modeling frequency and severity separately. It has also been a standard practice to assume, for simplicity, the independence of loss frequency and loss severity. However, in recent years, there is a sporadic interest in the actuarial literature and practice to explore models that depart from this independence assumption. Besides, because of the short-term nature of many lines of general insurance, the availability of data enables us to explore the benefits of using random effects for predicting insurance claims observed longitudinally, or over a period of time. This thesis advances work related to the modeling of compound risks via random effects. First, we examine procedures for testing random effects using Bayesian sensitivity analysis via Bregman divergence. It enables insurance companies to judge whether to use random effects for their ratemaking model or not based on observed data. Second, we extend previous work on the credibility premium of compound sum by incorporating possible dependence as a unified formula. In this work, an informative dependence measure between the frequency and severity components is introduced which can capture both the direction and strength of possible dependence. Third, credibility premium with GB2 copulas are explored so that one can have a succint closed form of the credibility premium with GB2 marginals and explicit approximation of credibility premium with non-GB2 marginals. Finally, we extend microlevel collective risk model into multi-year case using the shared random effect. Such framework includes many previous dependence models as special cases and a specific example is provided with elliptical copulas. We develop the theoretical framework associated with each work, calibrate each model with empirical data and evaluate model performance with out-of-sample validation measures and procedures.

Author: Siti Norafidah Mohd Ramli
Publisher:
ISBN:
Category : Copulas (Mathematical statistics)
Languages : en
Pages : 165

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"This PhD thesis seeks to offer a new framework that accommodates dependency in pricing an insurance portfolio following the renewal risk model, corporate bonds, as well as credit default swaps (CDS). This will be achieved by combining the approach and methodology of actuarial science with stochastic processes and probability theories, as well as employing a hint of the integral calculus used in the electromagnetic and viscoelasticity fields. [...]." -- Abstract.

Author: Emiliano A. Valdez
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Category :
Languages : en
Pages : 23

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For several years now, there continues to be attention in the modeling of insurance and other similar type of risks, such as the risk of credit default, to incorporate the presence of dependencies. Some of the early papers appearing in the literature demonstrate that for a typical portfolio of such risks, ignoring dependencies can have a direct impact on the tail or extremes of the resulting portfolio loss distribution. The tail of the loss distribution is something not to be ignored by the actuary or the risk manager. To date, in spite of this growing number of papers in the literature on dependence modeling, we find that there is no known published work that provides for an empirical evidence to validate the presence of dependencies in an insurance portfolio. In this paper, we use mixture models, customarily suggested to model dependent credit default risks, to facilitate the investigation of claim dependencies. The empirical data used to calibrate these models came from a portfolio of automobile insurance policies drawn from a randomly selected insurance provider. In order to measure the presence of claim dependencies, one of the most reasonable statistic to use is the relative risk ratio, a measure that is widely popular in medical statistics and is used to gauge how the claim occurrence of a particular insurance risk induces claim of another insurance risk. Our calibration results indicate some presence of positive dependencies; relative risk is in the neighborhood of 1.4 and resulting pair-wise correlation is 0.04. The model naturally extends to capture policyholder heterogeneity through the presence of co-variates by introducing mixture models with co-variates as explained in this article. Not surprisingly, because the premium is the actuary's best guess of the degree of riskiness of an insurance risk, at least on an a priori basis, it provides for the single most important factor that influences the presence of claim dependencies.