APPLIED MATHEMATICS (TURKISH, THESIS)
Master TR-NQF-HE: Level 7 QF-EHEA: Second Cycle EQF-LLL: Level 7

Course Introduction and Application Information

Course Code Course Name Semester Theoretical Practical Credit ECTS
AKB5004 Actuarial Risk Analysis Spring 3 0 3 8
This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester.

Basic information

Language of instruction: Turkish
Type of course: Departmental Elective
Course Level:
Mode of Delivery: Face to face
Course Coordinator : Dr. Öğr. Üyesi BAHAR KÖSEOĞLU
Recommended Optional Program Components: None
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.

Learning Outcomes

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.

Course Content

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.

Weekly Detailed Course Contents

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.

Sources

Course Notes / Textbooks: 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.

Evaluation System

Semester Requirements Number of Activities Level of Contribution
Homework Assignments 4 % 20
Presentation 1 % 10
Midterms 1 % 35
Final 1 % 35
Total % 100
PERCENTAGE OF SEMESTER WORK % 65
PERCENTAGE OF FINAL WORK % 35
Total % 100

ECTS / Workload Table

Activities Number of Activities Duration (Hours) Workload
Course Hours 14 3 42
Study Hours Out of Class 14 4 56
Presentations / Seminar 1 16 16
Homework Assignments 4 10 40
Midterms 1 20 20
Final 1 26 26
Total Workload 200

Contribution of Learning Outcomes to Programme Outcomes

No Effect 1 Lowest 2 Low 3 Average 4 High 5 Highest
           
Program Outcomes Level of Contribution
1) Ability to assimilate mathematic related concepts and associate these concepts with each other.
2) Ability to gain qualifications based on basic mathematical skills, problem solving, reasoning, association and generalization. 2
3) Be able to organize events, for the development of critical and creative thinking and problem solving skills, by using appropriate methods and techniques. 2
4) Ability to make individual and team work on issues related to working and social life.
5) Ability to transfer ideas and suggestions, related to topics about his/her field of interest, written and verball. 2
6) Ability to use mathematical knowledge in technology.
7) To apply mathematical principles to real world problems. 2
8) Ability to use the approaches and knowledge of other disciplines in Mathematics.
9) Be able to set up and develope a solution method for a problem in mathematics independently, be able to solve and evaluate the results and to apply them if necessary.
10) To be able to link abstract thought that one has to concrete events and to transfer the solutions and examine and interpret the results scientifically by forming experiments and collecting data. 3
11) To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively.
12) To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself,