Aktüerya Bilimleri BölümüAktüerya Bilimleri Bölümühttps://hdl.handle.net/11655/182024-03-29T13:53:59Z2024-03-29T13:53:59ZBağımlı Çoklu Yaşam Durumunda Stokastik Ölümlülük Yaklaşımları ve Aktüeryal FiyatlandırmaAktaş, Tuğbahttps://hdl.handle.net/11655/343092023-12-18T11:21:28Z2023-01-01T00:00:00ZBağımlı Çoklu Yaşam Durumunda Stokastik Ölümlülük Yaklaşımları ve Aktüeryal Fiyatlandırma
Aktaş, Tuğba
In this study, stochastic mortality approach is used to calculate the net single premiums of life products. Instantaneous mortality rates of individuals are modelled as time-changed Brownian motion. Here the time change is considered stochastically by means of subordinators. Subordinators are assumed to fit an inverse Gaussian distribution. Thus, the instantaneous mortality rates of individuals are assumed to follow a normal inverse Gaussian distribution. Parameter estimation was performed in such a way that the sum of squared errors between the Dabrowska estimate and the estimate of the joint survival function was minimised. The significance of the model was demonstrated using parametric and non-parametric approaches. The dependency structure between spouses is included in the model through subordinators. Marginal survival probabilities were obtained based on the estimated parameter values. Joint survival probabilities are calculated for both situations based on the assumption that individuals' future life times are dependent and independent. Then, according to the dependency structure of individuals, net single premium values for life annuities and life insurances are obtained in the multiple life situation. Finally, net annual premiums were calculated and the results were compared. Thus, the differences arising in actuarial calculations by taking into account the dependency between individuals are clearly seen.
2023-01-01T00:00:00ZGüvenilirlik Analizi ve Maliyete Etkisi : Elektronik Kartlar Üzerine Bır UygulamaKara, Melihhttps://hdl.handle.net/11655/341802023-12-01T07:54:44Z2022-01-01T00:00:00ZGüvenilirlik Analizi ve Maliyete Etkisi : Elektronik Kartlar Üzerine Bır Uygulama
Kara, Melih
Reliability theory has become an independent discipline in recent years for use in a
variety of fields, including mathematics, statistics, probability theory, and particularly
the actuarial sciences.In the actuarial sciences, the concept of reliability is used in life
and non-life insurance not only for estimating or calculating life probabilities, but also
for estimating the probability that a device will perform its duty without fail during its
lifetime.
The uncertainty of the death age of a person or the expiration of a system/part is
expressed with probability concepts. The most important of these concepts is life
analysis. Selection of the most appropriate life function and evaluation of the results of
use of the chosen life function are the leading factors that directly affect reliability in
survival analysis.
Products/portfolios or distributions with high reliability values have always been
preferred by customers or decision makers. In addition to reputation, repeat business,
customer requirements and competitive advantage, cost analysis also plays an important
role in making the concept of reliability stand out as an important feature in products.
Reliability data is used to examine the cost-effectiveness of products. In this thesis, the
concept of reliability and the life cycle of the product are examined in terms of
electronic cards, which are of great importance in defense industry.Electronic cards are
iv
one of the most important subsytems in all electronic systems. The reliability of the
system to which the electronic cards are connected precludes the expected economic
benefits in other sectors, especially in the defense industry.
In this study, in the reliability analysis of electronic cards, the exponential and Weibull
distributions, which are the most preferred but have a thin tail structure, as well as the
Lomax distribution, which has a thicker tail structure, are also examined. Mean square
error, maximum likelihood method and modified maximum likelihood method were
used for the estimation of Lomax and Weibull distribution parameters. In the
application part of the study, simulation technique was used to generate data on
electronic cards. The mean squared error was used as a criterion to compare the
methods used to estimate the parameters of the Lomax and Weibull distributions. The
simulation study was repeated for different sample sizes and different parameter values,
and conclusions were drawn. Reliability values were obtained under the assumptions of
exponential, Lomax and Weibull distributions for electronic board components and the
results were compared. In this study, the case of increasing the reliability value by
redundancy method was also examined. The effect of reliability values and redundancy
status examined in the study on the cost of the product was also examined and the
dimensions of the effect were shown as a result of the analysis. In this way, the
importance of the relationship between reliability and cost has been revealed.
2022-01-01T00:00:00ZBulanık-Rastgele Lee-Carter Modeli ile Ölümlülüğün ModellenmesiUçar, Ezgihttps://hdl.handle.net/11655/333612023-06-19T11:51:13Z2023-01-01T00:00:00ZBulanık-Rastgele Lee-Carter Modeli ile Ölümlülüğün Modellenmesi
Uçar, Ezgi
This thesis studies a fuzzy-random extension of the Lee-Carter model, which is one of the popular methods for modelling mortality rates. Age-related variables are fuzzified by using triangular fuzzy numbers and for this purpose a fuzzy regression model is developed and solved. The time-dependent variable is modelled as an ARIMA time series. After obtaining the fuzzy mortality rates, the associated probabilities of death and life expectancy were obtained. In the application part, the central mortality rates of the U.S. male population between 1970 and 2000 were used to predict the mortality rates for the next ten years. Finally, the obtained fuzzy results are defuzzified and compared with the Lee Carter model. In the comparison, it was concluded that the performance of the defuzzified central death rates was better.
2023-01-01T00:00:00ZKritik Hastalık Sigortalarında Saklı Markov ModeliAyrancı, Gönülhttps://hdl.handle.net/11655/270832022-12-01T12:29:39Z2022-01-01T00:00:00ZKritik Hastalık Sigortalarında Saklı Markov Modeli
Ayrancı, Gönül
In the literature, multi-state models are used in the calculations on critical illness insurance. In these models, in which the critical illness incidence rates are estimated, covariates can only be included after splitting into different group combinations due to the constraints of the method. This situation causes the data to be divided into too many sub-risk groups, inability to use continuous covariates and restriction in the validity of the results to a particular number of groups.
In this thesis it is aimed to propose a model that can be used in the pricing of critical illness insurance and considers the risk groups with a holistic perspective. For this purpose, using Hidden Markov Models (HMM) in modeling critical illness insurances is proposed. Incidence rates of critical illnesses are estimated for different risk groups with HMM.
This thesis uses the longitudinal panel data collected in The Health and Retirement Study (HRS) by Michigan University Social Research Institute. Using HRS data, parameters of both HMM and the orthodox models in the literature are estimated and their performances are compared. Results indicate that in most of the scenarios, the HMM model proposed in the thesis performs better than the Markov Model whose parameters are computed using Generalized Linear Model. Furthermore, premium calculations are done using Thiele’s differential equation and simulation method.
2022-01-01T00:00:00Z