Course Information


Course Information
Course Title Code Semester L+U Hour Credits ECTS
ACTUARIAL RISK THEORY UAKT401 7. Semester 2 + 2 3.0 6.0

Prerequisites None

Language of Instruction Turkish
Course Level Bachelor's Degree
Course Type Compulsory
Mode of delivery Oral presentation
Course Coordinator
Instructors Selin ÖZEN
Assistants
Goals The aim of this course is to introduce mathematical/probabilistic models for short-term insurance policies.
Course Content Loss distributions: lognormal, Pareto, Gamma distributions; reinsurance; fitting loss distributions to data; models for aggregate claims: Poisson distribution, negative binomial distribution; collective risk model: mean, variance, moment generating functions compound Poisson, compound binomial, compound negative binomial distributions; convolution and Panjer's recursion; individual risk model: mean, variance, security loading; ruin theory and Lundberg inequality.
Learning Outcomes 1) Construct models appropriate for short term insurance policies
2) Describe individual and collective risk models
3) Acquire formulae for the moment generating functions and moments of aggregate claims over a given time period
4) Derive a recursion formula for calculating the aggregate claims distribution for the collective risk model
5) Identify and describe the properties of several risk premium principles
6) Explain the concept of reinsurance
7) Explain the ruin theory according to Lundberg

Weekly Topics (Content)
Week Topics Teaching and Learning Methods and Techniques Study Materials
1. Week Introduction to risk theory Lecture; Question Answer; Problem Solving

 Presentation (Including Preparation Time)
2. Week Loss distributions: lognormal, Pareto, Gamma distributions, concept of reinsurance Lecture; Question Answer; Problem Solving

 Presentation (Including Preparation Time)
3. Week The collective risk model: introduction and the compound Poisson distribution Lecture; Question Answer; Problem Solving

 Presentation (Including Preparation Time)
4. Week The collective risk model: the compound binomial and the compound negative binomial distribution Lecture; Question Answer; Problem Solving

 Presentation (Including Preparation Time)
5. Week The collective risk model: aggregate claim distribution under proportional and excess of loss reinsurance Lecture; Question Answer; Problem Solving

 Presentation (Including Preparation Time)
6. Week Exact calculation of the aggregate loss distribution function for the collective risk model: convolution Lecture; Question Answer; Problem Solving

 Presentation (Including Preparation Time)
7. Week Exact calculation of the aggregate loss distribution function for the collective risk model: recursion formula Lecture; Question Answer; Problem Solving

 Presentation (Including Preparation Time)
8. Week Midterm exam

9. Week Approximate calculation of the distribution function for the collective risk model: normal and translated Gamma approximations Lecture; Question Answer; Problem Solving

 Presentation (Including Preparation Time)
10. Week The individual risk model: Introduction Lecture; Question Answer; Problem Solving

 Presentation (Including Preparation Time)
11. Week The individual risk model: Approximation by the collective risk model, calculation of probabilities Lecture; Question Answer; Problem Solving

 Presentation (Including Preparation Time)
12. Week Collective risk models over an extended period Lecture; Question Answer; Problem Solving

 Presentation (Including Preparation Time)
13. Week Collective risk models over an extended period and introduction to the ruin theory, ruin probability and claim amount distribution Lecture; Question Answer; Problem Solving

 Presentation (Including Preparation Time)
14. Week Ruin theory: the first surplus below the initial level Lecture; Question Answer; Problem Solving

 Presentation (Including Preparation Time)
15. Week Preparation for Final Exam Lecture; Question Answer; Problem Solving

 Presentation (Including Preparation Time)
16. Week Final exam


Sources Used in This Course
Recommended Sources
Bowers et al. (1997), Actuarial Mathematics, SOA Publications,US.
Dickson D.C.M. and Waters H.R. (1992), Risk Models, The Faculty of Actuaries and the Institute of Actuaries.
Dickson, D.C.M. (2004), Insurance Risk and Ruin, Cambridge University Press, Cambridge.

Relations with Education Attainment Program Course Competencies
Program RequirementsContribution LevelDK1DK2DK3DK4DK5DK6DK7
PY150000000
PY250000000
PY350000000
PY450000000
PY550000000

*DK = Course's Contrubution.
0 1 2 3 4 5
Level of contribution None Very Low Low Fair High Very High
.

ECTS credits and course workload
Event Quantity Duration (Hour) Total Workload (Hour)
Course Duration (Total weeks*Hours per week) 14 4
Work Hour outside Classroom (Preparation, strengthening) 14 4
Homework 4 3
Midterm Exam 1 2
Time to prepare for Midterm Exam 1 24
Final Exam 1 2
Time to prepare for Final Exam 1 24
Total Workload
Total Workload / 30 (s)
ECTS Credit of the Course
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Course Information
  • Course Information
  • Weekly Topics (Content)
  • Sources Used in This Course
  • Relations with Education Attainment Program Course Competencies
  • ECTS credits and course workload