Application of Risk Models to an Insurance Portfolio

Xinyi Xie

Master's thesis

Abstract:

For an insurance company, evaluating the aggregate claims distribution is needed. We can easily show how to apply the mixed distribution to the number claims and to the size of claims modelling. In this thesis, we use the mixed distribution in insurance practice as a probability distribution of two important variables. These are the claim numbers N and claim sizes X in different types of insurance portfolio of insurance policies. The key goal of this thesis is to compute the solvency capital requirement (SCR) of a insurance company and to determine the amount that company should hold for covering the total unexpected claims in one year duration. Different types of probability distributions of claim numbers and claim sizes are used in MATLAB, STATA and other programs. Despite the application part, the description of risk and insurance, as well as the description of individual risk model and collective risk model are introduced in Chapter 2. Then, the formula of each distribution, as well as description of maximum likelihood estimation and Monte Carlo simulation are all introduced in Chapter 3. The final result and the conclusion we draw are shown in the end of the thesis.

Abstract:

For an insurance company, evaluating the aggregate claims distribution is needed. We can easily show how to apply the mixed distribution to the number claims and to the size of claims modelling. In this thesis, we use the mixed distribution in insurance practice as a probability distribution of two important variables. These are the claim numbers N and claim sizes X in different types of insurance portfolio of insurance policies. The key goal of this thesis is to compute the solvency capital requirement (SCR) of a insurance company and to determine the amount that company should hold for covering the total unexpected claims in one year duration. Different types of probability distributions of claim numbers and claim sizes are used in MATLAB, STATA and other programs. Despite the application part, the description of risk and insurance, as well as the description of individual risk model and collective risk model are introduced in Chapter 2. Then, the formula of each distribution, as well as description of maximum likelihood estimation and Monte Carlo simulation are all introduced in Chapter 3. The final result and the conclusion we draw are shown in the end of the thesis.

Keywords

insurance risk, individual risk model, collective risk model, maximum likelihood estimation, Monte Carlo simulation, Poisson distribution, Negative binomial distribution, Normal distribution, Pareto distribution

Keywords

insurance risk, individual risk model, collective risk model, maximum likelihood estimation, Monte Carlo simulation, Poisson distribution, Negative binomial distribution, Normal distribution, Pareto distribution

Language used: English

Date on which the thesis was submitted / produced: 27. 4. 2018

Thesis defence

• Date of defence: 30. 5. 2018
• Supervisor: Jiří Valecký
• Reader: Ingrid Petrová

VŠB - Technical University of Ostrava

Ekonomická fakulta

Master programme / field:
Hospodářská politika a správa / Finance