Summer Projects (Msc Dissertations)

MSc in Actuarial Science

Summer Projects (MSc dissertations) Contents Page

Project 1 Bonus-Malus (NCD) Systems in Motor Insurance 1 Supervisor: Howard Waters

Project 2 Income Protection Insurance Claim Termination Rates by Cause of claim 2 Supervisor: Andrew Stott

Project 3 Minimum Variance Portfolios and the Wilkie Investment Model 3 Supervisor: Torsten Kleinow and Howard Waters

Project 4 Valuation of Guarantees, Hedging of Guarantees, Incompleteness 4 of Markets, Quantile Reserves Supervisor: David Forfar

Project 5 Practical Application/Results of Non-Life Mathematical Theory using R/Excel/VBA 6 Supervisor: David Forfar

Project 6 Fundamental Analysis of Company Shares 7 Supervisor: Brian Moretta

Project 7 Are Hedge Funds a Good Investment? 8 Supervisor: Brian Moretta

Project 8 Actuarial Modelling Using Bayesian Methods 9 Supervisor: George Streftaris

Project 9 Applications of R in Actuarial Science 10 Supervisor: Iain Currie

Project 10 Computational Bayesian Techniques for Censored and 11 Partially-Observed Processes Supervisor: Gavin Gibson

Project 11 Modelling Genetics and Insurance 12 Supervisor: Angus Macdonald

Project 12 Hitting Times for Levy Processes 13 Supervisor: Takis Konstantopoulos

Project 13 Hitting times for time-varying boundaries for Brownian motion 14 Supervisor: Takis Konstantopoulos

Project 14 Funding Methods for Pension Schemes 15 Supervisor: Jonathan Finn Project 1

Bonus-Malus (NCD) Systems in Motor Insurance Supervisor: Professor Howard Waters

Description Investigate Bonus-Malus systems from different countries. In particular, determine the "fairness" of different systems by investigating how well they differentiate between different levels of risk both with and without bonus hunger using different criteria for fairness.

Investigate the effect of bonus hunger using different assumptions about policyholder behaviour and/or different models for the number of claims.

Investigate how to model a UK protected NCD system within a Markov framework.

Computing Excel is sufficient for this project though other software may well be better.

Level of English required Moderate.

Supervisor availability No planned periods of absence. Project 2

Income Protection Insurance Claim Termination Rates by Cause of Claim Supervisor: Andrew Stott

Description Recent work by Dr Sing-Yee Ling, Professor Howard Waters and Professor David Wilkie has provided graduations of claim termination (death and recovery) rates for Income Protection insurance claims by cause of sickness.

The project will involve: a) Understanding Income Protection insurance b) Understanding the work by Ling, Waters and Wilkie c) Programming termination rates for different causes of sickness (Excel would be sufficient for this but other software may be better) d) Using these termination rates to calculate current claim annuities

Computing This project will involve a reasonable amount of computing. Excel would be sufficient for this but other software may be better.

Level of English Required Moderate.

Supervisor availability No planned periods of absence. Project 3

Minimum Variance Portfolios and the Wilkie investment Model Supervisors: Dr Torsten Kleinow and Professor Howard Waters

Description This project will involve: ia) Calculation of minimum variance portfolios for a given expected return. This is for a set of assets with specified means, variances and co-variances of returns over a single period and with no constraints on the holdings. b) Repeat i) with constraints on the holdings. c) Compare the solutions to i) and ii), particularly the holdings in the separate assets as functions of the target expected return. d) Learn about the Wilkie investment model and program it. e) Use the Wilkie model in one or more applications, for example: The calculation of minimum variance portfolios over a single period; Minimum variance of surplus portfolios given a specified future liability; The inclusion of a yield curve and the resulting arbitrage possibilities; Optimal multi-period investment decisions.

Computing Excel is sufficient for this project though other software may well be better.

Supervisor Availability At least one of the two supervisors will be available throughout the dissertation period. Project 4

Valuation of Guarantees, Hedging of Guarantees, Incompleteness of Markets, Quantile Reserves Supervisor: David Forfar

Description The ability to meet fairly (i.e. without adversely affecting the reasonable expectations of other policyholders) the financial guarantees, if these guarantees come into effect (i.e. ‘biting’ guarantees or guarantees that come ‘into-the-money’), is very important for life offices. The ability to hedge guarantees (or the economic impossibility of hedging e.g. in incomplete markets or if the life office does not go ‘short’) has been the province of quants/financial mathematics but it is now realised it should also have been the province of actuarial profession. The type and nature of financial guarantees is thus very important as the inability to meet ‘biting’ guarantees caused the demise of the oldest life assurance company in the world, Equitable Life founded in 1762. Students will study different types of guarantee in a with-profits fund, namely:- 1. A guaranteed maturity value (e.g. a sum of premiums to be paid over the policy’s life) for annual or regular premiums, 2. a guaranteed investment return each year (e.g. 4.5% each year) 3. an overall guaranteed investment return at maturity (e.g. (1.045)T where T is the term of the policy), 4. a guaranteed annuity rate (e.g. an annuity rate of 11.11%) applying to the guaranteed fund only (guaranteed fund=the sum assured increased by reversionary bonuses but excluding terminal bonus), 5. a guaranteed annuity rate (e.g. an annuity rate of 11.11%)applying to the full fund (i.e. the sum assured increased by reversionary bonuses and increased by endowment-style terminal bonus),

Computing Students will program in C++ (using the free Visual Studio 2008 which students can download from Microsoft – see below) to value the above guarantees (assuming the assets required are available on the stock-exchange) and then to show that the theoretically correct hedging investment strategy (students will determine what this is) reproduces the payoff from the guarantee no matter how stock-market behaves. Then the students will interface their programs with EXCEL using the xlw wrapper. Students will also look at the un-hedgeable aspects of guarantees (i.e. economic impossibility of hedging if the market is incomplete e.g. the stock market lacks longevity bonds, or if the life office’s investment strategy does not embrace going ‘short’) and sizeable effect that this has on the size of the life offices reserves which are required (i.e. so-called ‘quantile reserves’). This means that the life office’s financial strength is of paramount importance.

Computing A keen enthusiasm for high computing content and a willingness to learn C++ and interface with Excel is required. Suitable for students with good programming skills.

Level of English Required Above average facility with English is not required.

Supervisor Availability Planned absence of one week over the summer (to be confirmed).

References 1. The book Actuarial Mathematics for Life Contingent Risks (Chapter 13) 2. Students will model in C++ starting out with all the programs in Drs. Atchison and King’s Heriot-Watt C++ Course (available at: http://www.ma.hw.ac.uk/ams/msc_finmath/cppnotes.pdf) (The computer language C++ is the most common in investment banks for modelling derivatives), 3. A free compiler (Visual Studio 2008) for C++ can be downloaded from Microsoft under the Dreamspark program, see: Microsoft DreamSpark . Project 5

Practical Application/Results of Non-Life Mathematical Theory using R/Excel/VBA Supervisor: David Forfar

Description Students will study: (1) run-off triangles/chain-ladder methods whether using (a) inflation adjusted (b) average cost per claim (c) Bornhuetter-Ferguson or (d) loss ratio techniques. (2) risk theory (the risk that the experienced claims will exceed the resources of the general insurance company) (3) credibility theory (4) multiple-state Markov models for no-claims discounting (bonus-malus) (5) generalised linear models.

Computing The computing content will involve R/EXCEL/VBA and will require a laptop computer in order to derive practical results using R/EXCEL/VBA from the mathematical theory of non-life assurance.

Level of English Required Above average facility with English not required.

Supervisor Availability Planned absence of one week over the summer (to be confirmed).

References

1. Hossak I.B., Pollard J.H. and Zehnwirth B.(1983), Introductory statistics with applications in general insurance,Cambridge University Press. 2. Boland B. (2007), Statistical and Probabalistic Methods in Actuarial Science,Chapman Hall. 3. Tse Y-K, (2008) Non-life Actuarial Models, Cambridge University Press. 4. Hogg R.V. ad Klugman S. A. (1984), Loss Distributions, John Wiley Project 6

Fundamental Analysis of Company Shares Supervisor: Brian Moretta

Description One of the main methods of deciding which shares to invest in is fundamental analysis, where company financial statements are analysed and conclusions are drawn about the underlying business. By looking at the health of a company, its management and competitive advantages, comparing them with its competitors and expectations of the market, investors can come to conclusions about whether its shares will outperform the stock market.

Students will start by considering various valuation measures that can be put on companies and their usefulness in practice. This will introduce them to some different investment styles and consideration of how investment decisions are made.

Much of the project will consist of examining real companies, their sectors and operating environments to determine what is and isn't important for their investment case.

References ' The Intelligent Investor' - Benjamin Graham 'The Zulu Principle' - Jim Slater 'Accounting for Growth' - Terry Smith "The Cross-Section of Expected Stock Returns," (Fama & French), Journal of Finance, 47 (June 1992), 427-465.

Computing Students will not require a high level of computing for this project, but should be comfortable manipulating large amounts of data in spreadsheets.

Level of English Required Very high - the reporting that students will use will be written in English and they will be required to understand subtle nuances in statements.

Supervisor Availability No planned periods of absence. Project 7

Are Hedge Funds a Good Investment? Supervisor: Brian Moretta

Description The rise of the hedge fund industry in the last decade has been predicated on the idea of superior risk adjusted returns from an investment that has low correlation with more traditional asset classes. Indices of hedge fund performance have now existed for some time and could be used to consider whether this premise is correct.

This project will consist of two possible parts. The first will look at the returns hedge funds have provided relative to the risk incurred. Consideration will be given to the quality of the data available and whether the stated returns provide a good measure of the underlying risks.

The second part will consider the diversification benefits of hedge funds. Using Modern Portfolio Theory, students will construct efficient frontiers without and with hedge funds as a possible asset class. This should allow assessment of whether hedge funds do provide a good alternative to traditional investments.

Computing Very good computing skills will be required. A good knowledge of Excel will be an advantage, but knowledge may be acquired.

Level of English Required A reasonable level of English is required.

Supervisor Availability No planned periods of absence. Project 8

Actuarial Modelling Using Bayesian Methods Supervisor: Dr George Streftaris

Description In this project we will consider Bayesian methodology for modelling data arising in various areas of actuarial practice. The Bayesian approach is being increasingly used in actuarial science to tackle problems related to graduation of mortality rates, estimation of disease prevalence, analysis of overdispersed insurance claims, estimation of survival and loss distributions etc.

The project will suit students with a particularly strong background in statistics, who are also interested in applying modern statistical techniques in actuarial science. Some knowledge of Bayesian statistics is also important.

The main stages of the project will be: (a) Introduction to statistical models (e.g. generalised linear models (GLMs)) in actuarial Science; (b) Introduction to Bayesian statistics, Markov chain Monte Carlo methods and related software (WinBUGS, BOA); (c) Analysis of suitable data sets; (d) Writing up. Stages (a) and (b) will take the form of group work and may consist of a series of taught classes. Stages (c) and (d) will be performed individually.

References - Haberman, S. and Renshaw, A.E. (1996) Generalized linear models and actuarial science. The Statistician, 45 (4), 407-436. - Makov, U.E., Smith, A.F.M. and Liu Y.-H. (1996). Bayesian methods in actuarial science. The Statistician, 45 (4), 503-515. - Streftaris, G. and Worton, B.J. (2008) Efficient and accurate approximate Bayesian inference with an application to insurance data. Computational Statistics & Data Analysis 52, 2604-2622.

Computing Considerable computing effort will be required (about 50% of the work).

Level of English Required Adequate writing and English language skills are required.

Supervisor Availability Supervisor will be away for three weeks in July/August.

Project 9

Applications of R in Actuarial Science Supervisor: Dr Iain Currie

Description This project is suitable for someone with a strong interest in applying R to problems in Actuarial Science. There are many parts of the syllabus for the Diploma in Actuarial Science which would benefit from a more computer oriented approach. Graduation is one part where some efforts have been made but there are many others. There are obvious examples in Risk Theory: for example, aggregate claims processes and the impact of reinsurance can be studied using theory and simulation. No Claims Discount methods in non-life insurance is another area.

The project will consist of writing sets of R-functions which can be used as add-ons to courses. These functions would be delivered over the web and should be suitable for use by future generations of students (subject to obvious quality control!)

Computing Good knowledge required.

Required level of English A reasonable level of English is required.

Supervisor Availability Not available between 21-25 June, 30 June–9 July or 22-27 July. Project 10

Computational Bayesian Techniques for Censored and Partially-Observed Processes Supervisor: Professor Gavin Gibson

Description Thanks to computational Bayesian techniques it is now possible to fit nonlinear stochastic models for a variety of population processes, such as the spread of epidemics, when the processes are only partially observed or censored in some way. This project will look at a particular computational approach - namely Markov chain Monte Carlo methods - and show how it can be applied to fit models in some representative settings. The project will provide experience of using Bayesian methods, implementing modern computational methods, and of working with a range of data sets, including data on epidemics and on numbers of research grant awards to HWU over recent years.

Computing The students will require to do a considerable amount of R programming but will be given substantial help with this, and given guidance on programme structure. A considerable challenge will be to understand Markov chain Monte Carlo methods and to formulate samplers in mathematical terms to solve particular problems. A stong probabilistic and statistical background will be necessary.

Level of English Required There will be less of an emphasis on literature review, but students will be pointed towards some particular case studies from the literature, so English skills should be reasonably strong.

Supervisor availability Absent for around 2 weeks during the project period (to be confirmed)

Project 11

Modelling Genetics and Insurance Supervisor: Professor Angus Macdonald

Description The development of DNA-based genetic tests for gene mutations that may be associated with risk of disease has led to much discussion about the implications for life insurers. Genetic information is perceived by many to be extremely personal and private, so there is resistance to the idea that an insurer could be allowed to ask about genetic information as part of medical underwriting. However, insurers are concerned that if applicants for insurance possess information relevant to the risk that they need not disclose, adverse selection will arise. The risks involved, to individuals and to insurers, can only properly be assessed by setting up appropriate actuarial models. The aim of the project is, first, to review the subject and modelling approaches; and, second, to implement a model and address one or more of the problems found in this area.

Computing Numerical work will require some computing skills, either in Excel or in a programming language.

Level of English Required High level of English as considerable descriptive writing will be required

Supervisor Availability A 2-week absence during the summer to be confirmed. Project 12

Hitting Times for Levy Processes Supervisor: Professor Takis Konstantopoulos

Description This project deals with hitting time probabilities for Brownian motion and, more generally, Levy processes. A Levy process is a stochastic process with real values, stationary independent increments which is continuous in probability. Students will be asked to understand and evaluate characteristics of hitting times of such processes based on last path decomposition techniques. Examples include compound Poisson processes. The projects will be written in LaTeX (an introduction will be given). The required background is probability and stochastic processes.

Computing Nil.

Supervisor Availability Planned absences during mid and late June. Project 13

Hitting times for time-varying boundaries for Brownian motion Supervisor: Professor Takis Konstantopoulos

Description This project deals with hitting time probabilities of time-varying levels for Brownian motion, i.e. a pathwise continuous process with independent increments. Students will be asked to understand and apply versions of the strong Markov property in order to come up with equations for level hitting. The projects will be written in LaTeX (an introduction will be given). The required background is probability and stochastic processes.

Computing Nil.

Supervisor Availability Planned absences during mid and late June. Project 14

Funding Methods for Pension Schemes Supervisor: Jonathan Finn

Description In this project students will investigate the effects of different funding methods for pension funds. The students will simulate membership details for a pension Scheme, specify the benefits provided by the scheme, construct an appropriate service table and investigate the financial effects of the different methods. Part of the project will involve finding out what benefits are provided by real schemes.

Computing A considerable amount of numerical work will be involved. A spreadsheet would be the ideal platform.

Supervisor Availability No planned absences in the dissertation period