Course co-ordinator(s): Dr Abdul-Lateef Haji-Ali (Edinburgh), Dr Anke Wiese (Edinburgh).
Aims:
Given a portfolio of insurance policies the course aims:
- to develop models for the amount of a single claim from one policy in the portfolio, models for the number of claims from one policy in the portfolio, models for the total claim amount arising from the whole portfolio, in all cases with and without reinsurance,
- to study the probability that a portfolio will be insolvent,
- to estimate premiums using both claims experience and general information,
- to develop models for no claims discount,
- to show how simulation methods can be used to model insurance quantities.
Detailed Information
Course Description: Link to Official Course Descriptor.
Pre-requisites: none.
Location: Edinburgh.
Semester: 2.
Syllabus:
-
- Loss distributions:
- log normal, Pareto, gamma distribution
- reinsurance
- fitting loss distributions to data
- Models for aggregate claims:
- Poisson distribution, negative binomial distribution, binomial distribution
- collective risk model: mean, variance, moment generating function
- compound Poisson distribution
- the Normal approximation
- the translated gamma distribution
- Panjer’s recursion
- Calculating premiums using a security loading
- Ruin and simulation
- simulation, the inverse transform method
- using simulation to estimate probabilities
- using simulation to estimate the probability of ruin
- Run-off triangles
- estimating outstanding claims by chain ladder, average cost per claim, Bornhuetter-Ferguson methods
- Credibility theory
- Bayesian methods, loss functions
- Bayesian credibility: normal/normal model, Poisson/Gamma model
- empirical Bayes credibility: Model I (constant volume),
- No claims discount:
- NCD scales
- transition matrix, stable distribution
- bonus hunger
- Loss distributions:
Learning Outcomes: Subject Mastery
At the end of studying this course, students should be able to:
- Calculate the mean, variance and skewness of certain loss distributions.
- Calculate the effect of reinsurance on the distribution of claims.
- Calculate the mean, variance and moment generating function for the collective risk model.
- Use the compound Poisson distribution to describe aggregate claims.
- Use Panjer’s recursion to compute the exact distribution of aggregate claims.
- Understand the concept of ruin in the insurance setting and use simulation to estimate the probability of ruin.
- Assess future claims using chain ladder, average cost per claim and Bornhuetter-Ferguson methods.
- Use credibility theory to estimate premiums using (i) Bayesian methods (ii) empirical Bayes methods.
- Obtain the transition matrix for an NCD system and find the stable distribution.
Reading list:
-
- “Risk Models” by D C M Dickson and H R Waters. Available on VISION
- “Credibility Theory” by H R Waters. Available on VISION
- “Risk Modelling in General Insurance” by R J Gray and S M Pitts
- “Practical Risk Theory for Actuaries” by C Daykin, T Pentikainen and E Pesonen
- “Insurance Risk and Ruin” by D C M Dickson.
Assessment Methods: Due to covid, assessment methods for Academic Year 2021-22 may vary from those noted on the official course descriptor. Please see the Computer Science Course Weightings and the Maths Course Weightings for 2020-21 Semester 1 assessment methods.
SCQF Level: 11.
Other Information
Help: If you have any problems or questions regarding the course, you are encouraged to contact the lecturer
Canvas: further information and course materials are available on Canvas