# Statistics for Insurance (StatIns)

### Course content

This course provides students with a solid understanding and practical skills in statistical analysis for insurance data, with a specific focus on non-life insurance, reserving, and life insurance.

Students will explore key concepts, including non-life insurance distributions, maximum likelihood methods, non-life regression models and machine learning, model selection techniques, insurance data analysis using R, claims reserving with chain ladder models and alternative methods, multivariate counting processes, survival analysis models for insurance, as well as parametric and non-parametric estimation techniques.

The primary goal of this course is to help students effectively estimate and predict various types of risks, even in complex data scenarios, based on a strong theoretical foundation. Additionally, students will learn how to communicate the results of their models clearly. The course encourages critical thinking and the practical analysis of insurance-related data while maintaining a balance between theory and real-world application.

Education

MSc Programme in Actuarial Mathematics

Learning outcome

Knowledge:  At the end of the course, the student should develop the following:

• Throrough understanding of distributions in non-life insurance.
• Throrough understanding of maximum likelihood methods in non-life insurance.
• Basic understanding of the specificities of non-life regression models, and their practical ramifications.
• Thorough understanding of model selection methods.
• Familiarity with insurance data analysis and machine learning techniques, including implementation in R.
• Thorough understanding of claims reserving via classic chain ladder models.
• Basic understanding of claims reserving via alternatives to the chain ladder models.
• Basic understanding of multivariate counting processes.
• Thorough understanding of the basic models in survival analysis for insurance.
• Thorough understanding of non-parametric estimation: Nelson-Aalen and Aalen-Johansen estimators.
• Thorough understanding of parametric estimation and regression models in life insurance: MLE methods and Poisson regressions.

Skills: Students will develop a robust set of skills in non-life and life insurance data analysis, including claims reserving. They will gain the ability to bridge theory and practical application, acquiring the following specific skills:

• Proficiency in estimating and predicting risks, even when dealing with heavy-tailed data, censoring, truncation, or covariates, utilizing both parametric and non-parametric methodologies.
• Ability to estimate multi-state models, employing both parametric and non-parametric approaches.

Competences: Upon completion of the course, students will possess a broad foundation for statistically analyzing insurance-related data. They will have developed critical thinking skills, theoretical tools, and practical expertise to tackle diverse statistical challenges in insurance. Additionally, the students develop the following specific competences:

• Capacity to discern the appropriate technique for specific scenarios, as well as having an understanding of the strengths and limitations inherent in different modeling approaches.
• Effective communication of model outputs and diagnostic findings, both in technical and practical terms.

4 hours of lectures and 3 hours of exercises per week for 14 weeks.

Bachelor's degree in Actuarial Mathematics or similar is recommended. Furthermore, Mathematical Finance or Stochastic Processes in Continuous Time no later than at parallel is recommended.

Written
Oral
Individual
Collective
Continuous feedback during the course of the semester

Individual and written feedback in connection with the mandatory group project. Collective and oral feedback during exercise sessions and lectures.

ECTS
15 ECTS
Type of assessment
On-site written exam, 3 hours under invigilation
Continuous assessment
Type of assessment details
Two components, each counting for 50% of the final grade: About midway, an individual mandatory written project is assigned to the students. At the end of the course, a written 3 hours exam with written aids allowed. To pass the course, the students must pass both components.
Aid
Only certain aids allowed
• For the written exam, only written aids allowed.
• For the individual mandatory written project, all aids are allowed.
Marking scale
Censorship form
No external censorship
Re-exam

Same as the ordinary exam.

The student must hand in the re-exam individual mandatory written project at least 3 weeks prior to the re-exam.

If an individual mandatory written project or exam from the ordinary examination has a passing grade, it must be re-used.

If 10 or fewer students have registered for the re-exam, the written exam will be changed to oral exam. Duration: 30 min. No aids nor preparation time.

##### Criteria for exam assessment

See Learning outcome

Single subject courses (day)

• Category
• Hours
• Lectures
• 56
• Preparation
• 224
• Exercises
• 42
• Project work
• 50
• Exam Preparation
• 37
• Exam
• 3
• English
• 412

### Kursusinformation

Language
English
Course number
NMAK24005U
ECTS
15 ECTS
Programme level
Full Degree Master
Duration

2 blocks

Placement
Block 1 And Block 2
Schedulegroup
C
Capacity
No limitation – unless you register in the late-registration period (BSc and MSc) or as a credit or single subject student.
Studyboard
Study Board of Mathematics and Computer Science
##### Contracting department
• Department of Mathematical Sciences
##### Contracting faculty
• Faculty of Science