The goal of this course is to give an overview of the most important mathematical techniques used in (non-life) risk insurance. After finishing the course a student is able to
- explain the role of utility function in deciding premium for a risk and can calculate the insurance premium;
- explain different ways of modelling a risk and work with them to analyze the risk;
- analyze different risks, possibly in combination with further reinsurance, based on their ruin probabilities;
- explain and work with different premium principles for risk;
- analyze simple bonus-malus systems in risk insurance.
All of us come across different risks in our lives. We cover ourselves against those risks with insurances such as a life insurance, a health insurance, a car insurance, a fire insurance, etc. In this course, we shall deal with non-life insurance. The main difference between life insurance and non-life insurance contracts is the time aspect: the time span of a life insurance is usually a few decades whereas for non-life insurance it is mostly a year, although renewable every year.
We start with so-called utility theory to answer questions such as why or when would one buy an insurance? Or, from the insurance company's perspective, under what conditions should they start the business? Subsequently, you will get a taste of the commonly used probabilistic models of risks, namely, the individual model and the collective model. You will also learn the principles commonly used to fix a premium. During this process, the ruin probability of an insurer turns out to be an important factor. So we shall study the basics of ruin theory and also of reinsurance. Besides the standard theory of non-life insurance mathematics, we discuss some examples of methods that are directly relevant for actuarial practice such as bonus-malus systems.