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Dissertation presented as the partial requirement for obtaining a Master's degree in Statistics and Information Management, specialization in Risk Analysis and Management Accurate risk estimation with proportionate fees is the cornerstone of insurance activity, a billion-dollar service industry. Due to progressive technological development, insurance companies are now able to improve their risk assessment in the underwriting process of automobile insurance. Through the installation of Onboard-diagnostic devices or with an application in the customers’ smartphones, insurance companies may measure behavioral and situational risk factors such as distance covered and driving habits. These new risk factors provide further information that helps the client’s risk evaluation beyond the traditional risk factors of customer and car specific. The objective of this research is to measure the increased prediction capacity of the claim predicting model by including driver behavior variables. A Generalized Linear model was applied, that includes not only the traditional risk factors, but also additional risk factors measured by telematics, and a new model-based ensemble predictor to a dataset with more than 3 million drivers. Results show that the incorporation of driver’s behavior variables increases the overall capacity of the model. By adding these behavioral risk factors, the actuarial accuracy is increased, leading to a more tailored approach of risk assessment and also awarding the clients that have safer conduct on the road and penalizing those with a more hazardous behavior prone to incurring in car accidents.

Telematicsdevices installed in insured vehicles provide actuaries with new risk factors, such as the time of the day, average speeds, and other driving habits. This paper extends the multivariate mixed model describing the joint dynamics of telematics data and claim frequencies proposed by Denuit et al. (2019a) by allowing for signals with various formats, not necessarily integer-valued, and by replacing the estimation procedure with the Expected Conditional Maximization algorithm. A numerical study performed on a database related to Pay-How-You-Drive, or PHYD motor insurance illustrates the relevance of the proposed approach for practice.

Most insurance policies include a deductible, so that a part of the claim is assumed by the insured. In order to get a full coverage of the claim, the insured has two options: hire a Zero Deductible Insurance or take out an insurance policy with deductible and, simultaneously, a Refundable Deductible Insurance. The objective of this paper is to analyze these two options, comparing the premium paid. We define dif (F) as the difference between the premiums paid. This function depends on the parameters of the deductible applied, and we focus our attention on the sign of this difference and the calculation of the optimal deductible, that is, the values of the parameters of the deductible that allows us to obtain the greatest reduction in the global premium.

Pay-how-you-drive (PHYD) or usage-based (UB) systems for automobile insurance provide actuaries with behavioural risk factors, such as the time of the day, average speeds and other driving habits. These data are collected while the contract is in force with the help of telematic devices installed in the vehicle. They thus fall in the category of a posteriori information that becomes available after contract initiation. For this reason, they must be included in the actuarial pricing by means of credibility updating mechanisms instead of being incorporated in the score as ordinary a priori observable features. This paper proposes the use of multivariate mixed models to describe the joint dynamics of telematics data and claim frequencies. Future premiums, incorporating past experience can then be determined using the predictive distribution of claim characteristics given past history. This approach allows the actuary to deal with the variety of situations encountered in insurance practice, ranging from new drivers without telematics record to contracts with different seniority and drivers using their vehicle to different extent, generating varied volumes of telematics data., SCOPUS: ar.j, info:eu-repo/semantics/published

Pay-How-You-Drive (PHYD) or Usage-Based (UB) systems for automobile insurance provide actuaries with behavioral risk factors, such as the time of the day, average speeds and other driving habits. These data are collected while the contract is in force with the help of telematic devices installed in the vehicle. They thus fall in the category of a posteriori information that becomes available after contract initiation. For this reason, they must be included in the actuarial pricing by means of credibility updating mechanisms instead of being incorporated in the score as ordinary a priori observable features. This paper proposes the use of multivariate mixed models to describe the joint dynamics of telematics data and claim frequencies. Future premiums, incorporating past experience can then be determined using the predictive distribution of claim characteristics given past history. This approach allows the actuary to deal with the variety of situations encountered in insurance practice, ranging from new drivers without telematics record to contracts with different seniority and drivers using their vehicle to different extent, generating varied volumes of telematics data.

5510 sayılı Sosyal Sigortalar ve Genel Sağlık Sigortası Kanunu ile Genel Sağlık Sigortalısı olarak kapsama alınan yoksulların, hiçbir sosyal güvencesi olmayanların ve isteğe bağlı sigortalıların ödeyecekleri primin belirlenmesi için gelir seviyeleri, gelir testi ile tespit edilmektedir. Eğer kişi başına düşen gelir miktarı brüt asgari ücretin üçte birinden az ise birey yoksul sayılmakla birlikte primleri devlet tarafından karşılanmaktadır. Diğer gelir seviyeleri için ise farklı prim tutarları söz konusudur. Çalışmada, mevcut sistemde bireyler arasındaki eşitsizlikler ortadan kaldırılarak daha adil bir prim hesaplama sistemi oluşturulması amacıyla bulanık mantıktan faydalanılmıştır. Prim hesaplanmasında kullanılmak üzere kişi başına düşen aylık kullanılabilir gelir, aylık harcama miktarı ve yaş değişkenleri dilsel ifadelerle bulanıklaştırılmıştır. Ödenecek prim miktarları uzman görüşüne dayanan bulanık kural tabanı ile 2012 yılında TÜİK Hane halkı bütçe anketine katılan 4650 kişi için hesaplanmıştır. Daha sonra hesaplanan bu primler ağırlıklandırılarak Türkiye genelinde 9.749.855 yoksul, hiçbir sosyal güvencesi olmayan ve isteğe bağlı sigortalılardan toplanacak prim miktarları tahmin edilmiştir. Çalışma sonucunda kişi başına düşen gelir miktarını daha doğru yansıtan kişi başına düşen aylık kullanılabilir gelir kullanılarak belirlenen gelir seviyeleri dilsel ifadeler yardımıyla bulanıklaştırılarak daha adil derecelendirmeler sağlanmış ve bireyler arasındaki eşitsizlik giderilmiştir. Ayrıca yüksek gelirli isteğe bağlı sigortalıların avantajlı hale gelmelerini önlemek amacıyla ödenecek prim miktarları gelir ve harcamanın yanı sıra yaş değişkeni de kullanılarak daha adil olarak hesaplanmıştır. Önerilen model ile hesaplanan primler mevcut sistemde toplanan primlerle karşılaştırıldığında toplanan prim miktarı artmış, primleri devlet tarafından karşılanan bireylerin sayısı yaklaşık olarak aynı kalmıştır. Sonuç olarak bulanık kural tabanından faydalanılarak daha adil bir şekilde daha fazla prim toplanacağı sonucuna ulaşılmıştır.Anahtar Kelimeler: Bulanık Mantık, Bulanık Çıkarım Mekanizması, Genel Sağlık Sigortası, Prim For determination of premiums that have to be paid by poor, people without social security and voluntarily insured covered by the 5510 Social Insurance and General Health Insurance Law the income levels are ascertained via income tests. If per capita income is less than the one third of gross minimum wage, the person is considered as a poor while the premiums have been paid by the government. For other income levels different premiums are discussed. In this study, by determining the inequities among people in the current system, it is aimed to eliminate inequities and to establish a fairer premium system. For this reason fuzzy logic has been utilized. Monthly per capita disposable income, per capita expenses and age went through the process of fuzzification by linguistic concepts. Premiums have been calculated via fuzzy rules based on expert opinion for 4650 people who attended income survey of Turkish Statistical Institute (TSI). Then, total premium paid by the number of 9749855 people has been estimated by weighting the calculated premiums. As a result, monthly per capita disposable income which more accurately reflects income and which was scaled by the linguistic variables fairer gradation have been provided and inequities have been eliminated. In addition, besides income and expenses, age has been used for equitable calculation in order not to make voluntarily insured advantageous. When obtained results were compared with the total premiums collected in the current system, total premiums have been increased whereas the number of people who are supported by state approximately has been remained same. Eventually, by utilizing fuzzy rule base more premiums have been collected in a fairer way.Key Words: Fuzzy Logic, Fuzzy Inference System, General Health Insurance, Premium 152

Vasicek is one of the stochastic interest rate model that can capture interest rates movement. The aim of this research was to get the comparison of the level premium for an endowment life insurance under stochastic interest rate without and by using Monte Carlo simulation. The result show that the level premium without Monte Carlo simulation is not much different from the result of the level premium by using Monte Carlo simulation. However, the premium calculation by using Monte Carlo simulation can also be searched the range of losses and gains of the insurance company at certain confidence interval. In this case using a confidence interval of 95%.

Aktüerya bilimi makul beklentilerin gerçekleşmesini engelleyen tesadüfî olayların olumsuz yöndeki finansal etkisini azaltmak için bir mekanizma olarak tanımlanmıştır. Aynı türden tehlikeyle karşı karşıya olan kişilerin, prim olarak adlandırılan belirli bir miktar para ödemesi şeklinde toplanan bu tutarın, adil bir şekilde belirlenmesi sigorta şirketleri için önemli bir konudur.Bu çalışmada temel amaç, adil bir prim fiyatlama yapabilmek için portföyü oluşturan bireylere ilişkin risk faktörlerini dikkate alan matematiksel ve istatistiksel temellere dayanan bir model oluşturmaktır. Bu nedenle öncelikle prim fiyatlamaya temel oluşturan modeller incelenmiş daha sonra poliçe sahiplerinin risk faktörlerini de dikkate alan etkili bir model elde etmek için Genelleştirilmiş Lineer Modeller kullanılmıştır. Yapılan analizler sonucunda en iyi sonuç veren Logaritmik Bağlı Gama Model kullanılarak hasar tahminleri yapılmış ve veri setini oluşturan müşteriler için risk değerlendirmesi yapılmıştır. Actuarial Science is described as a mechanism that decreases the negative financial effects of random events which becomes obstacles to actualize reasonable expectations. It is important subject to make a fair share for the same amount of money which is paid by the people who has the same risk.In this dissertation, main goal is to form a model that?s based on mathematic and statistic and takes into account risk factors for the individuals in the portfolio to be able to make fair rating. In this reason, it is used generalized linear model to be able to form effective model. Finally, risk assessment were made using Logarithmic Gamma Model which gives the best results of the analysis for the customers that forms the data set. 118

The portfolio consistency fund studied in the paper is referred to a pension scheme of beneficiaries entering in the retirement state at the same time. It arises from the payment stream consisting in cash flows due at the beginning of each year in case of life of the pensioner: in the deferment period, in the form of premiums entering in the fund, and during the retirement period, in the form of instalments getting out of it. The fund dynamic as function of the time of valuation evolves increasing thanks to the interest maturing on the accumulated fund and decreasing because of the benefits paid to the survivals. Both the mortality trend, determining the number of payments at each time, and the interest maturing on the fund, are considered deterministically unknown at the moment of the contract issue. Stochastic assumptions about the behaviour of the interest rate process and the description of the mortality trend betterment, most likely to be expected in very long periods and in civilized world, provide a dynamic description of the pension scheme and in particular of the pension fund. In the paper we want to deepen the aspect of the financial and demographic basis chosen for premium calculation with respect to the impact on the portfolio fund consistency and on the risk arising from the randomness in the choice of the survival model used for the valuations. To this aim, we will assume for the fund description different projection levels for the survival probabilities and the Vasicek hypotheses for the interest rates maturing on the fund itself; moreover, we will determine the premium amounts introducing different scenarios in a safety loading perspective. As evident, in the premium quantification lower interest rate jointly with higher survival probabilities constitute a form of implied loading. The numerical application presented in the paper shows how the change in the premium calculation conditions affects the portfolio fund consistency in the different scenarios and investigates on the impact they have on the Demographic Model Risk Measure. Useful information for managing aim can be derived. © 2009 IOS Press. All rights reserved.

IV ÖZET Bu çalışmada sorumluluk sigortalarında, özellikle Türkiye'de zorunlu olarak yapılması gerekli karayolları trafik kanunu zorunlu mali sorumluluk sigortası için primin doğru tespit edilmesinde kullanılabilecek bir metot araştırılmıştır. Zorunlu mali sorumluluk sigorta tarifesi, şu anda yasa gereği Başbakanlık Hazine Müsteşarlığınca hesaplanmakta olup; araçların kullanım tarzlarına göre belirlenmiş standart primlerden oluşmaktadır. Araştırma sonucunda, sigortacıya nakit akış riski ve zamanla birlikte piyasadaki faiz oranım da dikkate alarak yeterli bir geri dönüş sağlayan finansal modelleme tekniklerinden biri olan Myers-Cohn modelinin trafik sigortasına uygulanabileceği gözlenmiştir. Ayrıca model üzerinde bulanıklığın ortadan kaldırılmasını sağlamak amacıyla bulanık kümeler tekniği kullanılarak model yemden çözümlenmiş ve her iki modelin trafik sigortasına adaptasyonunu sağlayan birer bilgisayar programı hazırlanmıştır. ABSTRACT In this thesis, a method is established to calculate the correct premium for the mandatory traffic liability insurance, which is an important necessity for Turkey. Up to date, mandatory liability insurance premium is the responsibility of Prime Ministery The Undersecretariat of Treasury by law and is calculated as a standart premium according to the way of vehicle useage. In this study, it is shown that Myers-Cohn model, one of the financial modelling techniques, can be applied to the traffic insurance. This model supplies enough income after taking into consideration of the cash flow risk, the time and the interest rate. In addition fuzzy set theory is used to avoid fuzziness and the computer programs are prepared to adapt these two models to traffic insurance. 48