The binomial model; risk-neutral pricing of derivative securities; introduction to Ito's formula and SDEs; stochastic asset models; Black-Scholes model; arbitrage and hedging; interest-rate models; actuarial applications.

Topics include collective risk model, calculation of moments and mgf of aggregate claims, recursion formulae, effect of reinsurance; individual risk model, De Pril's recursion formula; fundamentals of decision theory; credibility theory; exact credibility and the Buhlmann-Straub model; basics of ruin theory.

Topics include insurance markets and products; underwriting and risk assessment; policy design; actuarial modelling; actuarial assumptions and feedback; reserving methods.

This subject provides students with the experience of carrying out research independently on each of three topics chosen by the subject’s lecturers. It involves a two-semester program of study, (students must enrol in the subjects in two consecutive semesters). For each topic, the student is required over eight weeks to conduct and present as an extended essay the results of an independent piece of actuarial science research.

Topics considered in this subject include premium principles, including variance principle, Esscher principle, risk adjusted principle; applications of utility theory, premium calculation and optimal reinsurance retention levels; reinsurance problems; ruin theory, Lundberg's inequality, explicit solutions for the probability of ultimate ruin, application of Panjer's recursion formula, the probability and severity of ruin, the effect of reinsurance on ruin probabilities.

This subject will consider the following topics: No-arbitrage pricing in continuous-time models. Completeness. Fundamental Theorem of Asset Pricing. Applications of martingales. Multidimensional Brownian motion in asset price models. Other asset price models. Pricing of path-dependent options. Computation methods.

A research essay not exceeding 10,000 words on a topic approved by the Head of Department. The word count includes bibliography, footnotes, appendices and the number of words which would take up space used for tables, formulae and charts.

Refer to ACTL90016 Actuarial Science Research Report Part 1 for details

Analysis of investment portfolios and asset classes from the perspective of an appointed actuary, with a view to identifying assets that suit the requirements of a variety of general insurance, life insurance, superannuation and other defined benefit liabilities.

Topics include assessment of solvency; analysis of experience; analysis of surplus; actuarial techniques in the wider fields; and an introduction to professionalism.

Normally topics will include current techniques used in forecasting in finance, accounting and economics such as regression models, Box-Jenkins, ARIMA models, vector autoregression, causality analysis, cointegration and forecast evaluation, ARCH models. The computer software used is EVIEWS.

The overall aim of this subject is to introduce students to the essential concepts and techniques/tools used in Bayesian inference and to apply Bayesian inference
to a number of econometric models. Basic concepts and tools introduced include joint, conditional and marginal probability distributions, prior, posterior and predictive
distributions, marginal likelihood and Bayes theorem. Key tools and techniques introduced include Markov chain Monte Carlo (MCMC) techniques, such as the Gibbs and Metropolis Hastings algorithms, for model estimation and model comparison and the estimation of integrals via simulation methods. Throughout the course we will implement Bayesian estimation for various models such as the traditional regression model, panel models and limited dependent variable models using the Matlab programming environment.

Numerical techniques focuses on the theory and application of numerical methods for solving financial problems. The applications may include option valuation, value at risk, term structure modelling, portfolio simulation and optimisation and capital budgeting. These applications motivate the study of matrix methods, the solutions of linear and nonlinear equations, interpolation and approximation methods, numerical integration and Monte Carlo methods. No prior programming experience is required as the principles of programming are covered.

Modern science and business makes extensive use of computers for simulation, because complex real-world systems often cannot be analysed exactly, but can be simulated. Using simulation we can perform virtual experiments with the system, to see how it responds when we change parameters, which thus allows us to optimise its performance. We use the language R, which is one of the most popular modern languages for data analysis.

The theory of statistical inference is important for applied statistics and as a discipline in its own right. After reviewing random samples and related probability techniques including inequalities and convergence concepts the theory of statistical inference is developed. The principles of data reduction are discussed and related to model development. Methods of finding estimators are given, with an emphasis on multi-parameter models, along with the theory of hypothesis testing and interval estimation. Both finite and large sample properties of estimators are considered. Applications may include robust and distribution free methods, quasi-likelihood and generalized estimating equations. It is expected that students completing this course will have the tools to be able to develop inference procedures in novel settings.

Risk management is a key business activity that impacts the full range of organisational activities and functional areas across the enterprise. This subject surveys a spectrum of business risks from operational to strategic risks. It provides a foundation in enterprise risk management principles, tools and techniques such as risk scenario planning.

Topics include the Australian General Insurance industry and products, actuarial estimation of claims cost, general insurance liabilities, general insurance pricing, capital management, accounting and regulatory reporting.

Computing techniques and data mining methods are indispensable in modern statistical research and data science applications, where “Big Data” problems are often involved. This subject will introduce a number of recently developed methods and applications in computational statistics and data science that are scalable to large datasets and high-performance computing. The data mining methods to be introduced include general model diagnostic and assessment techniques, kernel and local polynomial nonparametric regression, basis expansion and nonparametric spline regression, generalised additive models, classification and regression trees, forward stagewise and gradient boosting models. Important statistical computing algorithms and techniques used in data science will be explained in detail. These include the bootstrap resampling and inference, cross-validation, the EM algorithm and Louis method, and Markov chain Monte Carlo methods including adaptive rejection and squeeze sampling, sequential importance sampling, slice sampling, Gibbs sampler and Metropolis-Hastings algorithm.

Computing techniques and data mining methods are indispensable in modern statistical research and data science applications, where “Big Data” problems are often involved. This subject will introduce a number of recently developed methods and applications in computational statistics and data science that are scalable to large datasets and high-performance computing. The data mining methods to be introduced include general model diagnostic and assessment techniques, kernel and local polynomial nonparametric regression, basis expansion and nonparametric spline regression, generalised additive models, classification and regression trees, forward stagewise and gradient boosting models. Important statistical computing algorithms and techniques used in data science will be explained in detail. These include the bootstrap resampling and inference, cross-validation, the EM algorithm and Louis method, and Markov chain Monte Carlo methods including adaptive rejection and squeeze sampling, sequential importance sampling, slice sampling, Gibbs sampler and Metropolis-Hastings algorithm.