The University of Southampton
Courses

# STAT6075 Statistical Methods in Insurance

## Module Overview

### Aims and Objectives

#### Module Aims

To explain the need for short term insurance contracts and to look at the ways in which insurance contracts are written, including the operation of re-insurance arrangements. To use statistical models to describe methods for determining both premiums and effective re-insurance arrangements. To introduce the use of generalised linear models, decision theory and time series in insurance.

#### Learning Outcomes

##### Learning Outcomes

Having successfully completed this module you will be able to:

• Understand the definitions of some basic insurance terms, particularly those relating to short-term contracts
• Understand the main concepts underlying the analysis of time series and how to apply them
• Use Monte Carlo simulation to estimate quantities of interest in models used for insurance
• Apply problem solving and numerical skills
• Understand the properties of some loss distributions: gamma, exponential, Pareto, generalised Pareto, normal, log-normal, Weibull and Burr, and how to fit them to complete claim size data
• Understand how simple forms of proportional and excess of loss re-insurance are arranged
• Model the distribution of the aggregate claims for both the insurer and the re-insurer, particularly using the compound Poisson distribution
• Understand the concept of ruin in a risk model
• Apply techniques for analysing run-off triangles and projecting the ultimate position.
• Use Bayesian approaches to credibility theory to calculate premiums in general insurance
• Demonstrate knowledge and understanding of the concepts of decision theory and how to apply them
• Demonstrate knowledge and understanding of the fundamental concepts of generalised linear models and how they may be applied

### Syllabus

Review of distribution theory; loss distributions; risk models – collective and individual; re-insurance; ruin theory; run-off triangles; Bayesian credibility theory; decision theory; generalised linear models; time series; random number generation and Monte Carlo simulation.

#### Special Features

This module may lead to an exemption from Subject CT6, Statistical Methods, of the joint examinations of the Institute and Faculty of Actuaries

### Learning and Teaching

TypeHours
Teaching45
Independent Study105
Total study time150

Chatfield, C. (2004). The Analysis of Time Series.

Dobson, A. J (2001). An Introduction to Generalized Linear Models.

The Faculty of Actuaries and The Institute of Actuaries (2009). Subject CT6 Core Reading: Statistical Method.

Boland, P. J. (2007). Statistical and Probabilistic Methods in Actuarial Science.

Klugman, S. A., Panjer, H. H. and Willmot, G. E. (2004). Loss Models: From Data to Decisions.

Dickson, D. C. M. (2005). Insurance Risk and Ruin.

### Assessment

#### Summative

MethodPercentage contribution
Assignment 5%
Assignment 5%
Class Test 5%
Class Test 5%
Exam  (3 hours) 80%

#### Referral

MethodPercentage contribution
Exam 100%

#### Repeat Information

Repeat type: Internal & External

Pre-requisite: MATH6122

### Costs

#### Costs associated with this module

Students are responsible for meeting the cost of essential textbooks, and of producing such essays, assignments, laboratory reports and dissertations as are required to fulfil the academic requirements for each programme of study.

In addition to this, students registered for this module typically also have to pay for:

##### Books and Stationery equipment

You will require a copy of Formulae and Tables for Actuarial Examinations 2002, 2nd edition, the "Gold Book".

Please also ensure you read the section on additional costs in the University’s Fees, Charges and Expenses Regulations in the University Calendar available at www.calendar.soton.ac.uk.

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