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School of Mathematics

# MATH69531 - 2012/2013

General Information
• Title: General Insurance
• Unit code: MATH69531
• Credits: 15
• Prerequisites:
• Co-requisite units: None
• School responsible: Mathematics
• Member of staff responsible: Dr. Kees van Schaik
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Other Resources
• Materials will be available in lectures.

## Specification

### Aims

The unit aims to provide students a grounding in modern stochastic modelling techniques of particular relevance to general non-life insurance.

### Brief Description of the unit

In insurance offices the basic blocks of business are portfolios of policies that make up branches within the insurance firm such as fire, motor, property etc. For each portfolio, claims come in at random and each claim involves a random amount. For the insurance company to remain solvent it must understand the process generating the claims (the claim number process) and the claim size process in order to assess and compare risks that will enable it to calculate competitive premiums. The course looks at different possible stochastic models for these processes and at the effect of different types of reinsurance on the reserves behind a portfolio of policies.

### Intended Learning Outcomes

Upon successful completion, the students are expected to be able to

• demonstrate a good understanding of the basic concepts and results in the mathematics of
1. modelling loss distributions,
2. modelling the Claim Number process,
3. risk models for the Aggregate claim amount,
4. re-insurance strategies,
5. incurred but not reported (or settled) claims,
6. Monte Carlo simulation techniques;
• formulate, solve and interpret stochastic problems in a non-life insurance context and show judgement in the selection and application of appropriate tools and techniques;
• solve problems using logical thinking and the appropriate tools and techniques of probability theory and statistics;
• demonstrate a capacity for analytical thinking and ability to use probabilistic concepts in real life situations.

### Syllabus

1. Utility functions, risk aversion, use of utility models in insurance; loss functions, zero-sum two-person games, statistical games, decision functions, optimal decisions, minimax criterion. Bayes criterion. [4]
2. Loss distributions (L.D) in insurance; parametrized families of L.D and estimation of the parameters, heavy tailed 3. Re-insurance strategies; Excess of loss (stop-loss) re-insurance, proportional re-insurance, proportional re-insurance, policy excess. [7]
3. Features of short term contracts in general insurance. [1]
4. Risk models of short term general insurance.
1. The Collective risk model ; Modelling the claim Number process, the Aggregate claim process. The compound Poisson model, the compound Binomial model, the compound Negative Binomial Model.
2. Individual risk model.
Re-insurance in risk models. Parameter uncertainty (accident proneness).
Computational methods in calculating the aggregate claim distribution in risk models.
1. Panjer's recursive algorithm.
2. Approximate methods. [15]
5. Incurred but not reported/settled techniques: Chain ladder method, The average cost per chain method, the Bornhuetter-Ferguson method. Adjustments for inflation. [3]
6. Monte Carlo simulation techniques: acceptance-rejection method, variance reduction techniques, error estimates. [3]

### Teaching and learning methods

1. Lectures and Feedback Tutorials: There are three lectures and one tutorial class each week.
2. Private Study: In addition, students should expect to spend at least four hours each week on private study for this course unit.

### Assessment

Coursework 20%
Examination at the end of the semester, two and a half hours duration, 80%.

## Arrangements

Materials will be available in lectures.