| MATHEMATICS (TURKISH, PHD) | |||||
| PhD | TR-NQF-HE: Level 8 | QF-EHEA: Third Cycle | EQF-LLL: Level 8 | ||
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| AKB5004 | Actuarial Risk Analysis | Fall | 3 | 0 | 3 | 8 |
| The course opens with the approval of the Department at the beginning of each semester |
| Language of instruction: | Tr |
| Type of course: | Departmental Elective |
| Course Level: | |
| Mode of Delivery: | Face to face |
| Course Coordinator : | Dr. Öğr. Üyesi BAHAR KÖSEOĞLU |
| Course Lecturer(s): |
Prof. Dr. İRİNİ DİMİTRİYADİS |
| Course Objectives: | The objective of this course is to develop proficiency in the application of models used for insurance losses and show how these models are used to assess insurance premiums. Students will also be able to solve specialised insurance problems and explain the assumptions underlying different statistical models. |
|
The students who have succeeded in this course; Be able to model frequency and severity, model total claims distributions, calculate discrete and continuous time ruin probability and analyse the effect of actuarial decisions on the probability of ruin. The student will also be introduced to the principles of credibility theory and will have an understanding of its areas of use; will know about basic loss reserving methods and apply to different sets of data. |
| Frequency and severity models; compound distributions, calculations of moments, conditional moments, discrete time ruin probability, continuous time ruin probability, Lundberg's inequality, bayesian estimation and credibility; claims reserving for non-life insurance. |
| Week | Subject | Related Preparation | |
| 1) | Review of probability. Discrete and continuous random variables and their distributions. | ||
| 2) | Measures of location and dispersion. Expectation and moments. Moment generating functions. | ||
| 3) | Loss Distributions. | ||
| 4) | Conditional distributions, conditional expected value and variance. Methods of creating new distributions. Prior and posterior distributions. | ||
| 5) | Point estimation and method of moments. Maximum likelihood and confidence intervals. Fitting loss distributions. | ||
| 6) | Aggregate loss models, the compound model for aggregate claims.Computing the aggregate loss distribution. | ||
| 7) | The individual and collective risk models. | ||
| 8) | Distribution of the aggregate claim amount. Compound Poisson models, recursive formula, approximations.Introduction to ruin problems. | ||
| 9) | Ruin probability in the short term, factors effecting probability of ruin.Effect of reinsurance. | ||
| 10) | Continuous time ruin models. The Poisson process, Lundberg's inequality and the adjustment coefficient. | ||
| 11) | Introduction to credibiity theory. Classical credibility, full and partial credibility. Aims of credibility models. | ||
| 12) | Credibility theory continued. Bayesian credibility. Bühlmann and Bühlmann and Straub models. | ||
| 13) | Experience rating and bonus malus systems. | ||
| 14) | Review and applications. | ||
| 15) | Final exam. | ||
| 16) | Final exam. | ||
| Course Notes: | Hossack, I., Pollard, J,H., Zehnwirth, B., ‘Introductory statistics with applications in general insurance’. Klugman, S., Panjer, H., Willmot, G., (2004) Loss Models, From Data to Decisions,John Wiley and Sons. |
| References: | Daykin, C, Pentikainen, T., Pesonen, M.(1994) Practical Risk Theory for Actuaries, Chapmann and Hall. Werner, G., Modlin, C, Basic Ratemaking, CAS study notes. |
| Semester Requirements | Number of Activities | Level of Contribution |
| Attendance | % 0 | |
| Laboratory | % 0 | |
| Application | % 0 | |
| Field Work | % 0 | |
| Special Course Internship (Work Placement) | % 0 | |
| Quizzes | % 0 | |
| Homework Assignments | 4 | % 20 |
| Presentation | 1 | % 10 |
| Project | % 0 | |
| Seminar | % 0 | |
| Midterms | 1 | % 35 |
| Preliminary Jury | % 0 | |
| Final | 1 | % 35 |
| Paper Submission | % 0 | |
| Jury | % 0 | |
| Bütünleme | % 0 | |
| Total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 65 | |
| PERCENTAGE OF FINAL WORK | % 35 | |
| Total | % 100 | |
| Activities | Number of Activities | Duration (Hours) | Workload |
| Course Hours | 14 | 3 | 42 |
| Laboratory | 0 | 0 | 0 |
| Application | 0 | 0 | 0 |
| Special Course Internship (Work Placement) | 0 | 0 | 0 |
| Field Work | 0 | 0 | 0 |
| Study Hours Out of Class | 14 | 4 | 56 |
| Presentations / Seminar | 1 | 16 | 16 |
| Project | 0 | 0 | 0 |
| Homework Assignments | 4 | 10 | 40 |
| Quizzes | 0 | 0 | 0 |
| Preliminary Jury | 0 | ||
| Midterms | 1 | 20 | 20 |
| Paper Submission | 0 | ||
| Jury | 0 | ||
| Final | 1 | 26 | 26 |
| Total Workload | 200 | ||
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution |