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  1. Tez No: 42183
  2. Yazar: SELİM AREN
  3. Danışmanlar: Y.DOÇ.DR. ŞAHAMET BÜLBÜL
  4. Tez Türü: Yüksek Lisans
  5. Konular: Sigortacılık, Insurance
  6. Anahtar Kelimeler: Belirtilmemiş.
  7. Yıl: 1995
  8. Dil: Türkçe
  9. Üniversite: Marmara Üniversitesi
  10. Enstitü: Sosyal Bilimler Enstitüsü
  11. Ana Bilim Dalı: Sigortacılık Ana Bilim Dalı
  12. Bilim Dalı: Belirtilmemiş.
  13. Sayfa Sayısı: 153

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Özet (Çeviri)

CONTENTS 1. Introduction I 2. Insurance - Statistics Relation V 3. Risk And Probability VII 3.1. Risk And Types Of Risk VII 3.2. Probability VIII 3.2.1. Basic Concepts About Probability VIII 3.2.2. Import Distributions Of Probability IX 3.2.2.1. Normal Distribution IX 3.2.2.2. Binominal Distribution X 3.2.2.3. Poisson Distribution X 3.2.2.4. Tschebycheff Inequality XI 4. Multivariate Statistical Methods XII 4.1. Principle Component Analysis XII 4.2. Factor Analysis XIII 4.3. Cluster Analysis XIII 5. Application Of Multivariate Analysis Methods In The Insurance Profession XV 5.1. Principle Component Analysis XV 5.1.1. Evaluation Of The Principle Component Analysis For 52 Insurance Companies XV 5.1.2. Evaluation Of The Principle Component Analysis For 40 Insurance Companies Excluding Those Of Life Insurance XVI 5.1.3. Evaluation Of The Principle Component Analysis For 12 Life Insurance Companies XVII 5.2. Factor Analysis XVIII 5.2.1. Evaluation Of The Factor Analysis For 52 Insurance Companies XVIII 5.2.2. Evaluation Of The Factor Analysis For 40 Insurance Companies Excluding Those Of Life Insurance XX 5.2.3. Evaluation Of The Factor Analysis For 12 Life Insurance Companies XXI 5.3. Cluster Analysis XXII 5.3.1. Evaluation Of The Cluster Analysis For 52 Insurance Companies XXII 5.3.2. Evaluation Of The Cluster Analysis For 40 Insurance Companies Excluding Those Of Life Insurance XXIII 5.3.3. Evaluation Of The Cluster Analysis For 12 Life Insurance Companies XXIV 6. General Evaluation XXVII1. INTRODUCTION The concept of insurance, as an inherent result of its own nature, always implicates both twin notions of uncertainty and risk. The corporations that are specialized in the profession of insurance are founded with the constitutional aim of doing business under certainty and providing services for clients which themselves do business or live under uncertainty and risk that future brings to ali of us. In this concern, the point of concentration in the profession of insurance, surely is, to make relevant and realistic estimates about what the future will bring us, by challenging the problems of uncertainty and risk that obscure the human capacity of imagination. Uncertainty is present for all the situations where the information of which is not available for the decision makers which should decide on a deal and which desire to minimize the being risky of the issue. Nevertheless, the lack of information is an insurmountable obstacle when the data which are sought is related with unrealized matters of future days or years. Thereupon, the data of past or present times, which are collected much more easily, or in some cases, completely, can be and are used by making projections, for the production of scenarios concerning the future reality.II In this conjunction, the estimations about future are heavily bound to the well-keeping of statistical records concerning past and present events. Nevertheless, collecting and keeping data are not enough to foresee and overcome the uncertainty and being risky of the coming days. Data collection and book keeping are prerequisites of challenging the obscurity of future. On the other hand, the statistical records about past and present realities are themselves only the raw materials of estimations. The process of estimation which is a crucial field of insurance industry is obviously nothing but making statistical analyses. As it is clear the science of statistics is a very important component of the insurance business. The researcher has aimed at signifying the importance and relevance of statistical methods in the insurance business. As it is known, the science of statistics provides us with measurable and then comparable tools called variables. By using variables we may discover many scientific results concerning the activities of the insurance companies and their efficiency. In this thesis, the goal is to classify the insurance companies in groups using 9 variables which are the data from the characteristics of companies. A further theme is (if possible) to diminish the number of variables withoutdiminishing the main results provided by these 9 variables and to realize what those selected variables out of nine are. This type of statistical analysis has two very important and useful outcomes : first of all, this study is a guide for the newcomer corporations of the insurance sector. Every newcomer may have different goals while entering a new sector ; either becoming the leader company of the industry or a follower firm. In the light of this statistical analysis, a newcomer company according to its own goals of achievement, can decide in which range its variables should be set. Accordingly, the company is informed about the special effects of different variables on the position of the companies in the insurance sector and then the newcomer firm can adjust the values of its variables so that it can settle on a position it sees as suitable. The second but not a less significant advantage resulted from this study is the exploration of the most important variables about the insurance sector. The researchers who decide to work on similar topics may use the opportunity of working with fewer variables selected out of nine variables of this study. This paper consists of six sections. The first section is the introduction, the second is dedicated to the explanation of insurance-statistics relations. The third section is about risk and types of probability.IV The fourth section is reserved for the explanation of theories of principles component analysis, Factor Analysis and Cluster Analysis, all of which are utilized in this study. The fifth section is for the exhibition of the results and, the sixth and last section is the chapter of general evaluation of all the thesis.V 2. INSURANCE - STATISTICS RELATION Statistics is a science which facilitates decision making concerning future by analyzing today with the help of quantitative methods. Statistics has significant relations with both scientific research and business life. It is possible to classify the usage of statistics in the insurance sector into three groups : 1. Estimates of Future 2. Determination of Standards 3. Control of Standards Estimates of Future : Each insurance company manager desires to know about future, how much premium will be produced, how much damage will be paid, how much of it should be reassured and in how many years catastrophic risks are repeated ? To know all of these is possible only if right statistical data are collected and kept orderly.VI Determination of Standards: How much premium will be asked and for what type of risk ? To make the big numbers law functional, what should be the necessary amount of production ? To answer such questions, statistical technique are necessary. Control of Standards: By using statistical technique, it can be easier to decide whether the difference between determined standards and achieved results.VII 3. RISK AND PROBABILITY Insurance is the ensuring power against losses caused by uncertainty and risk. Insurance companies decide under risk and the decision they make is a result of probability calculations. In the insurance sector, risk and probability are two very important concepts. In this section of this research, risk, types of risk, probability and distributions of probability will be explained. 3.1 Risk and Types of Risk Risk is a situation where loss and damage are possible and probable Risks are divided into two groups in the insurance sector : 1. Risks of insured individuals 2. Risk of insured companies Risks of insured individuals are divided into five kinds of risk : -death -infirmity (defectiveness) -elderliness -unemploymentVIII -legal responsibility Risks of insured companies are divided into four kinds of risk : -death and infirmity -legal responsibility -commodity damage -indirect damage 3.2 Probability Probability is the ratio of the desired number events to the total number of events. Probability varies between 0 and 1. If the probability is 1, it means that this event will happen unconditionally. If the probability of an event is 0, this event can not be realized at all. 3.2.1. Basic Concepts About Probability Simple event is a situation where desired results are achieved by only one try. Complex event is a situation where more than one result is achieved by only one try.IX Independent event is an event which does not affect and is not affected by another event. Dependent event is an event, the happening of which is due to or hindered by the happening of another event. Conditional probability is the probability of being hindered of a dependent event by the happening of another event. 3.2.2 Important Distributions of Probability The past motion of an event is the distribution of this event. Special distributions are found by observations of distribution of every event. 3.2.2.1 Normal Distribution Laphe and Gauss are two researchers who worked on the variance of errors of measurement. They found that the variance in the errors of measurement almost always draws a bell shaped curve. They called it the normal curve. Characteristics of the normal distribution : 1. Units are distributed by chance 2. Distribution is symmetric 3. Distribution is continuous4. Average and standard deviation vary according to the number of units 5. Average is calculated by number of units. 3.2.2.2 Binominal Distribution X, n is the number of results which are of the type of results which are interested, encountered in an independent experiment. To obtain results which are of the type interested, in only one experiment has a probability called p, and to obtain other types of results has a probability of 1-p. In this case, X is called Binominal Random Variable only if the following conditions are met: 1. Number of experiment (n) is constant 2. There are only two situations for every experiment 3. The probability to obtain desired results is p, and to obtain other results is 1-p. 4. Experiments are independent from each other. 3.2.2.3 Poisson Distribution Poisson Distribution is a probability distribution used to determine the number of events happened is a specific volume, specific place or specific period of time.XI Characteristics of Poisson Distribution : 1. Poisson Distribution counts the number of happenings of a special event in a specific period of time, place, or volume. 2. Probability of happening of a special event, for all the units, is the same in a specific period of time, place, or volume. 3. The number of happened events in a specific unit of time, place, and volume is different from other units of time, place, and volume. 4. Average or expected number of events in each unit is I. 3.2.2.4 Tschebycheff Inequality Tschebycheff Inequality is a method to provide appropriate distribution for the randomly selected variables with the help of standard deviation and variance.XII 4. MULTIVARIATE STATISTICAL METHODS In the contemporary world, multivariate statistical methods are utilized in almost every area of business and science. These methods are also used in this thesis ; especially the Principal Component Analysis, Factor Analysis and Cluster Analysis. 4.1 Principle Component Analysis In an analysis, 'n' unit of different data can be analyzed according to 'p' unit of variables or characteristics. If the number of variables is higher, then the probability of coming together of related variables, and the correlation among them are higher. Principle Component Analysis is applied in order to get rid off these unacceptable effects. This analysis provides a smaller number of variables, with the help of a limited confiscation of the explanation ratio. Thereupon, the benefits of this method are both to get rid off related variables and to shrink the scale of analysis. Consequently, these provide easiness in processing and evaluating data and stronger reliance on results.XIII Principle Component Analysis has become a highly preferred test, thanks to the recently emerged possibilities of its multipurpose usages. 4.2 Factor Analysis The goal in applying the Factor Analysis is to define the covariance relations among many variables as random but unobservable and countable units called factors. Groupings are done concerning covariances among variables and inter-group covariance is smaller. Factor is a linear composition of observed variables. In the application of the Factor Analysis, it is aimed at obtaining new and fewer variables called factors by using the covariance matrix and without causing data loss. Factors are artificial but assumed inherent in the system. The most fundamental assumption iş that observable variables are a linear function of the unobservable but predictable variables. 4.3 Cluster Analysis Cluster Analysis is applied to classify ungrouped data by using the similarities among them and to obtain summary information about them.XIV In the Cluster Analysis, the number of classes are unknown at the beginning. Indeed, if it is known there is no need for making the Cluster Analysis. The principle target in the Cluster Analysis is to classify the data. The other targets are as followings: 1. To identify real types 2. To facilitate the model adaptation 3. To foresee groups 4. To testify hypotheses 5. To clarify data structure 6. To shrink data 7. To find inappropriate values In the theory of the Cluster Analysis, a normal distribution of data is a prerequisite. However in practice, being normal of only the distance values is seen as 'sufficient' condition.XV 5.APPLICATI0N OF MULTIVARIATE ANALYSIS METHODS IN THE INSURANCE PROFESSION In this thesis, analyses are done according to the following nine variables: G : Number of agencies X1 : Number of university graduate personnel / total number of personnel X2: Investment revenue / total investment X3: Total profit X4: Capital X5: Cash + Stocks (Free) + Bonds (Freee) X6: Stocks (Blocade) + Bonds (Blocade) X7: Technical profit X8: Domestic premium collection 5.1. Principle Component Analysis 5.1.1. Evaluation of The Principle Component Analysis For 52 Insurance Companies As a result of the Principle Component Analysis done for 52 Insurance Companies, it has been found that the first and second variables are effective. The sum of explanation ratio of the first and second variables is 67%.XVI By using Variamax Convergence, it has been found the same two variables as being effective, however this time their total expiation ratio is 60%. By using Quartimax Convergence, it has been found only one meaningful eigenvalue and the expiation ratio being 57.863%. By using Equamax Convergence, it has been found seven meaningful variables ratio of which is 67!268%. According to those outcomes, the best result is the result obtained before convergence analyses. 5.1.2. Evaluation Of The Principle Component Analysis For 40 Insurance Companies Exlcuding Those Of Life Insurance As a result of the Principle Component Analysis done for 52 Insurance Companies, excluding life insurance companies, it has been found that the fisrt and second variables are meaningful and their sum of explanation ratio is 72%.XVII If the Equamax Convergence the same two variables as before converging and their sum of explanation ratio is 62.774%. By using Quartimax Convergence, it has been found only one important eigenvalue and its explaination ratio is 65.281%. If the second variable is added, their explaination ratio becomes 71.045% However, as its is above mentioned, the explaination ratio before any convergence is 72%. As in brief, we many canclude that the most prefered result is obtained without any convergence. Another important outcome is that the two variables. Another important outome is that the two variables which are found important as a result of the Principle Component Analysis for 40 campanies are the same as the two variables found important as a result of the same Analysis for 52 companies. 5.1.3. Evaluation Of The Principle Component Analysis For 12 Life Insurance Companies As a result of the Principle Component Analysis for 12 Life Insurance Companies, It has been found that the first and second variables are important and their sum of explanation ratio is 83%.XVIII By using Equamax Convergence, it has been found that seven variables are important and the sum of their explaination ratio is 92.638%. By using Varimax convergence, it has been found that two variables are important and the sum of their explaination ratio is 92.186%. By using Varimax convergence, it has been found that two variables are important and the sum of their explaination ratio is 80.833%. As it is clearly seen, the most appropriate result is obtained by Principle Component Analysis without any Convergence. Another important finding is that in each of the tree Principle Component Analysis, the important variables are found as the same two variables. Therefore, we conclude that it is unnecessary to classify insurance companies as life and other insurance companies before the analysis data. 5.2. Factor Analysis 5.2.1. Evaluation of The Factor Analysis For 52 Insurance Companies As a result of the Factor analysis done for 52 insurance companies, it has been found that there are four factors and their sum of explaination ratio is 74.327% without any convergence.XIX By using the Equamax Convergence, it has been found that there are seven factors and their sum of explaination ratio is 65.427% which is too small to accept. By using Varimax Convergence, it has been found that there are four factors and their sum of explaination ratio is 70.163%. By using Quartimax Convergence, it has been found that there are four factors and their sum of explaination ratio is 70.163%. By using Quartimax Convergence, it has been found there are four factors and their sum of explaination ratio is 72.876%. As it is dearly seen, the best result is obtained without using any convergence in the initial Factor Analysis.XX 5.2.2. Evaluation of The Factor Analysis For 40 Insurance Companies Excluding Those Of Life Insurance As a result of the Factor Analysis for 40 insurance companies excluding the companies of life insurance, it has been found that there are two factors and their sum of explaination ratio is 68.702%. By using Varimax Convergence it has been found that there are six factors and their sum of explaination ratio is 66.719%. By using Equamax Convergence it has been found that there are four factors and their sum of explaination ratio is 76.728%. By using Quartimax Convergence it has been found that there are two factors and their sum of explaination ratio is 68.190%. The aim is to explain more much using with fewer variables. If this is not possible, the researher will decide to use small number of variables, or a small ratio of explaination. In our case, the smallest number of variables which is two is achieved both by the Quartimax Convergence and by the simple Factor Anaysis without convergence. Meanwhile, the highest explaination ratio isXXI obtained by the Varimax Convergence. Though, to decide is up to the researher. 5.2.3. Evaluation of The Factor Analysis For 12 Life Insurance Companies As a result of the Factor Analysis done for 12 life insurance companies, it has been found that there are two factors and their sum of explaination ratio is 88.130%. By using Equamax Convergence, it has been found that there are seven factors and their sum of explaination ratio is 92. 475%. By using Varimax Convergence, it has been found that there are four factors and their sum of explaination ratio is 90.475%. By using Quartimax Convergence, it has been found that there are three factors and their sum of explaination ratio is 85.517%. As it is clearly seen, the explaination ratios are nearly equal, and all of the smallest number of factors were obtained by the simple Factor Analysis without covergance.XXII The common result shared by the Factor Analysis done either for 52,40 and 12 insurance companies have two significant characteristics: First; in all the analyses the factor of“ Investment revenue / Total income”is a unique factor of its own. Secondly; the variables of“Total income”and“Cash + Stock (Free) + Bonds (Free) ”in most of the analysis results are in the same factors. As a general result of the Factor analysis, contradicting with the result of the Principle Component Analysis on the same issue, it has been concluded that to classify insurance companies in two groups such as life and other insurance companies is a helpful classification to obtain healthier outcomes. 5.3. Cluster Analysis 5.3.1. Evaluation Of The Cluster Analysis For 52 Insurance Companies As a result of the Cluster Analysis done for 52 insurance companies, it has been found that there are two clusters. In this first Cluster Analysis, no number of cluster is given before analysis. In the first found cluster there are gathered small insurance companies; and in the secondly found cluster there are gathered big insurance companies.XXIII As a result of another Cluster Analysis in which, this time, the number of clusters, being three, is given, it is found that the first cluster again contains all the small insurance companies, however the second cluster excludes one of its big companies; and this big company called 'Anadolu Hayat“ Insurance Company constitutes, on its given third cluster. As a result of a third Cluster analysis in which, this time, the number of clusters is taken to as four, it is found that the relatively biggest companies of the first cluster -in other words, the cluster of the small companies - leave this cluster to form new clusters. 5.3.2. Evaluation Of The Cluster Analysis For 40 Insurance Companies Excluding Life Insurance Companies As a result of Cluster Analysis done for 40 insurance companies, it has been found that there are again two clusters. In this first Cluster Analysis done for 40 insurance companies, no number of clusters is given before starting the analysis. The first cluster of the found two clusters, is again the cluster of small insurance companies and the second cluster of the found two clusters is also again the cluster of big insurance companies.XXIV As a result of the repeated form of the Cluster Analysis, in which, this time, the number of clusters is given before starting the analysis. The given number of clusters is three. In this case, it has been found that the cluster of small companies is divided into two and the cluster of big companies remain undivided. The new cluster which is formed by the division of the first cluster, contains relatively bigger companies of the group of small companies. As a result of the thirdl repeated form of the Cluster Analysis, in which, this time the given number of clusters is four, it has been found that the results are almost the same as the Cluster Analysis with three clusters for forty companies. However, the only difference is the formation of the fourth cluster. The fourth cluster is the cluster of only one insurance company which is called ”Halk Sigorta“ Insurance Company. This is a big company which leaves the cluster of big companies to form the fourth cluster. 5.3.3. Evaluation Of The Cluster Analysis For 12 Life Insurance Companies As a result of the Cluster Analysis done for 12 Life Insurance Companies, it has been found that there are again two clusters. In this first Cluster Analysis done for 12 life insurance companies, no number of clusters is given before starting the analysis. The interesting point in the findings isXXV that the first found cluster consists of eleven life insurance companies and the second cluster contains only one life insurance companies which is called ”Anadolu Hayat“ Life Insurance Company. As a result of the Cluster Analysis done for 12 Life Insurance Companies, when the number of clusters is given before starting the analysis as three clusters, it has been found that there are a third cluster which is again a cluster of one life insurance company. This new cluster is obviously formed as a result of a division from the first cluster. The name of the company which shapes the third cluster is ”Halk Yaşam“. As a result of the third repetation of the Cluster Analysis for 12 Life Insurance companies, in which this time, the given number of clusters is four, it has been found that the first three clusters are the same as before. The newly formed fourth cluster is again a cluster of only one insurance company leaving the first cluster. The name of the company which shapes the fourth cluster is ”Şark Hayat“. As a general result of the Cluster Analyses, done separately for 52, 40, and 12 insurance company, it has been seen that the effective variables in all the analyses are the same. It has been also understood that to classifyXXVI insurance companies into two groups as life and non - life insurance companies before analyzing is unnecessary for The Cluster Analyses done for 52 insurance companies by deciding the number of clusters to be four.XXVII 6. GENERAL EVALUATION This research is dedicated to highlight the importance of statistics in the insurance profession. The specific goals are to classify insurance companies into groups by using nine variables being data about special characteristics of these companies; to diminish - if possible - the number of variables without diminishing the main results which are provided by these nine variables which are sufficient to provide the main results. A further companies into two groups as life and non - life insurance companies or not. Three analyses are applied in this research. They are Principle Component Analysis, Cluster Analysis and Factor Analysis. It has been found that there is no need to divide insurance companies into two groups as life and non - life insurance companies while practising the Analyses Of Principle Component and Cluster. On the other hand it has been seen that the Factor Analysis necessitates this classification of life and non - life insurance companies. The Principle Component Analysis has given the results that there are two significant variables in the analysis of both life and non - life insurance branches of the insurance sector. The first significant variable is the number ofXXVIII agencies and the second is the ratio of university graduate personnel to the total number of personnel. This second finding is really an important issue which shows that the entry of university graduates to the insurance sector which used to be heavily employed by high school graduates, seems to improve the performance of the companies. The Factor Analysis has given the results that the variable which is called the Investment Revenue / Total investment ”in other words, Investment Profitablity has a unique characteristic and should be evaluated as every significant prerequisite of performance appraisal. The Cluster Analysis has shown that the companies in the insurance sector ought to be classified into four categories.

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