The increase in the use of copulas has introduced implementation issues for both practitioners and researchers. One of the issues is to obtain a copula function for a given set of data. The most common approaches for the estimation of the parameters of the copula functions have been the Maximum Likelihood Estimator (MLE) and the Inference Functions for Margins (IFM) methods. Archimedean copulas are one of the most important classes of copulas that are widely used in both finance and insurance for modelling dependent risks. However, simulating multivariate Archimedean copulas has always been a difficult task as the number of dimensions increases. The assessment of capital requirements has always been an important application of stochastic modelling. Capital requirements can vary significantly depending on the model adopted. Several professional bodies have recently discussed the concept of dependencies between insurance risks. They suggest that insurers should use a technique based on copulas to describe the dependence of risks within an insurance company in the context of solvency assessment. The first contribution of this thesis is to provide an insight into the efficiency of parameter estimation methods. This thesis uses numerical experiments to assess the performance of the two common approaches. The second contribution of this thesis is to present a new algorithm to simulate multivariate Exchangeable Archimedean copulas. This algorithm provides a practical solution for simulating one-parameter multivariate Archimedean copulas. Numerical experiments are used to apply this algorithm to determine the "additional" economic capital for an insurance company with multiple lines of business that wants to expand its business by adding another line of business and where the businesses are dependent. The third contribution of this thesis is to quantify the impact of the choice of copulas on the solvency measure of a general insurer within a Dynamic Financial Analysis modelling framework. The results of our experiments provide important guidance for the capital assessment for general insurers.

The increase in the use of copulas has introduced implementation issues for both practitioners and researchers. One of the issues is to obtain a copula function for a given set of data. The most common approaches for the estimation of the parameters of the copula functions have been the Maximum Likelihood Estimator (MLE) and the Inference Functions for Margins (IFM) methods. Archimedean copulas are one of the most important classes of copulas that are widely used in both finance and insurance for modelling dependent risks. However, simulating multivariate Archimedean copulas has always been a difficult task as the number of dimensions increases. The assessment of capital requirements has always been an important application of stochastic modelling. Capital requirements can vary significantly depending on the model adopted. Several professional bodies have recently discussed the concept of dependencies between insurance risks. They suggest that insurers should use a technique based on copulas to describe the dependence of risks within an insurance company in the context of solvency assessment. The first contribution of this thesis is to provide an insight into the efficiency of parameter estimation methods. This thesis uses numerical experiments to assess the performance of the two common approaches. The second contribution of this thesis is to present a new algorithm to simulate multivariate Exchangeable Archimedean copulas. This algorithm provides a practical solution for simulating one-parameter multivariate Archimedean copulas. Numerical experiments are used to apply this algorithm to determine the "additional" economic capital for an insurance company with multiple lines of business that wants to expand its business by adding another line of business and where the businesses are dependent. The third contribution of this thesis is to quantify the impact of the choice of copulas on the solvency measure of a general insurer within a Dynamic Financial Analysis modelling framework. The results of our experiments provide important guidance for the capital assessment for general insurers.

published_or_final_version / Statistics and Actuarial Science / Master / Master of Philosophy

The theme of the work is credit risk insurance. The main objective is to analyze this specific type of insurance, define its role in insurance system and for covering credit risk. Analyzed are both commercial insurance and insurance with state support. The important part of this work is also analysis of czech and world insurance markets and influence of global economic recession. At the end of the work there are presented alternative instruments for minimizing credit risk and their comparison with insurance products.

Thesis supervisor: Qihe Tang. Includes bibliographic references (p. 111-116).

(Uncorrected OCR) Abstract of the thesis entitled ON INSURANCE RISK MODELS WITH CORRELATED CLASSES OF BUSINESS submitted by Wu Xueyuan for the degree of Doctor of Philosophy at The University of Hong Kong in February 2004 In this thesis, we focus on ruin analysis of risk models wIth correlated classes of insurance business. Specifically, five risk models with different dependence relations between classes are introduced. For these models, various problems related to ruin probability are considered. vVe first study a continuous-time correlated aggregate clmms model with Poisson and Erlang risk processes. In this model, we assume that two classes of business are correlated through a common Erlang component in thelf claim-number processes. We derive an explicit expression for the mfimte-time survival probability of the assumed model when claim SIzes are exponentially distributed. For general claim-size distributions, we obtain some result for the infinite-time ruin probabIlIty, and present a numerical method for evaluating the probability of rum. Based on the continuous-tIme model of Yuen and "Vang (2002) with thin- ning correlatIOn, we propose a new dependence relatIOn with interaction between classes of business in the discrete-time case. Two dIscrete-time risk models with such a relation of dependence are studied. For the first interaction model: we investIgate the statIstical properties of the aggregate claIms for a family of claimnumber distributions. \Ve also compare the model with other existing models with correlated aggregate claIms in terms of the finite-time and infimte-time ruin probabllitles. The second model extends the interaction dependence to the case of the compound binomlal model with delayed claims. For this model, we develop a recursive method to compute the finite-time survival probabilities: and derive an explicit expression for the infinite-time survival probability in a special case. The last two risk models proposed in this thesis are the bivariate compound binomial model and the bivariate compound Poisson model. In the bivariate case: vanous definitions of ruin can be considered. For the bivariate compound binomial model, recursive algorithms for calculating several kinds of finite-time survival probability are presented and numerical examples are given. As for the bivariate compound Poisson model, we study the probabllity that at least one of the two classes of business will get ruined. Since this bivanate ruin probability is very dlfficult to deal with, we use the result of the bivariate compound binomial model to approximate the desired bivanate finite-time survlval probability. \Ve also obtain an upper bound for the infinite-time ruin probability via some association properties of the model. For a simplified version of the model, we examine 'l'l the mfimte-time ruin probability when claIm sizes are exponentially distributed. / abstract / toc / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

published_or_final_version / abstract / toc / Statistics and Actuarial Science / Master / Master of Philosophy

The goal of the project was to use the data in the Workers' Compensation Board (WCB) of British Columbia's data warehouse to develop a statistical model that could predict on an ongoing basis those short-term disability (STD) claims that posed a potential high financial risk to the WCB. We were especially interested in identifying factors that could be used to model the transition process of claims from the STD stratum to the vocational rehabilitation (VR) and long term disability (LTD) strata, and forecast their financial impact on the WCB. The reason for this focus is that claims experiencing these transitions represent a much higher financial risk to the WCB than claims that only progress to the health care (HC) and/or the short term disability (STD) strata. The sample used to investigate the conversion processes of claims consists of all STD claims (323,098) that had injury dates between January 1, 1989 and December 31, 1992. Although high-risk claims represent only 4.2 % of all STD claims, they have received 64.3% ($1.2 billion) of the total payments and awards ($1.8 billion) made to July 1999. Low-risk claims make up 95.8% of all the claims but only receive 35.7% ($651 million) of the payments and awards. Moreover, the average cost of high-risk claims ($86,200) is 41 times higher than the average cost of low-risk claims ($2,100). The main objective of the project was to build a reliable statistical model to identify high-risk claims that can be readily implemented at the WCB and thereby improve business decisions. To identify high-risk claims early on, we used logistic regression modeling. Since ten of the most frequently observed injury types make up 95.72% of all the claims, separate logistic regression models were built for each of them. Besides injury type, we also identified STD days paid and age of claimant as statistically significant predictors. The logistic regression models can be used to identify high-risk claims prior to or at the First Final STD payment date provided we know the injury type, STD days paid and age of claimant. The investigation showed that the more STD days paid and the older the injured worker, the higher the probability of the claim being high-risk.

This thesis is concerned with utilizing new mathematical techniques developed in Sweden for inverting characteristic functions of probability distributions of functionals defined on the collective risk stochastic process. A characteristic function is a Fourier transform. However, such transforms-could not be inverted. With the advent of the electronic computer, the Fast Fourier Transform technique was developed for inverting Fourier Transforms. Essentially these techniques replace integrals over an uncountable number of points by series over a discrete set of points. This thesis will convert some Swedish results into useful forms for American students. It will be concerned with the probability distribution of aggregate claims in a fixed time, as well as ruin probabilities. The thesis will illustrate the basic mathematical techniques with several practical problems. Computer programs and numerical examples will be included.

Thesis (M. Com.)--University of Canterbury, 2009. / Typescript (photocopy). "March 2009." Includes bibliographical references (leaves 81-82). Also available via the World Wide Web.