Subject Intended Learning Outcomes (SILO) #
To view the subject objectives and the generic skills you will develop through successful completion of this subject, please see the University Handbook.
ACTL30007 SILO #
The ACTL30007 subject intended learning outcomes (SILO) are as follows:
- Apply relevant pre-requisite knowledge of mathematics, probability theory and statistics in the solution of a range of practical problems.
- Derive and calculate probabilities for, and moments of, loss distributions both with and without simple reinsurance arrangements.
- Estimate the parameters of a loss distribution when data is complete or incomplete.
- Fit a statistical distribution to a dataset and perform goodness-of-fit tests.
- Construct risk models appropriate for short term insurance contracts and derive both moments and moment generating functions for aggregate claim amounts under these models with and without simple forms of proportional and excess of loss reinsurance.
- Derive recursion formulae and apply approximation methods to calculate aggregate claims distributions.
- Describe and apply copulas to model dependent risks.
- Apply extreme value theory in modelling the distribution of severity of loss.
- Describe and apply the main concepts and properties underlying the analysis of several time series models.
ACTL90020 SILO #
The ACTL90020 subject intended learning outcomes (SILO) are as follows:
- Apply relevant pre-requisite knowledge of mathematics, probability theory and statistics in the solution of a range of practical problems.
- Derive and calculate probabilities for, and moments of, loss distributions both with and without simple reinsurance arrangements.
- Estimate the parameters of a loss distribution when data is complete or incomplete.
- Fit a statistical distribution to a dataset and perform goodness-of-fit tests.
- Construct risk models appropriate for short term insurance contracts and derive both moments and moment generating functions for aggregate claim amounts under these models with and without simple forms of proportional and excess of loss reinsurance.
- Derive recursion formulae and apply approximation methods to calculate aggregate claims distributions.
- Describe and apply copulas to model dependent risks.
- Introduce extreme value theory and its applications in modelling the distribution of severity of loss.
- Explain and concepts and general properties of several time series models.
Mapping to the IFoA Actuarial Statistics 2 (CS2) subject #
This subject is one of three subjects covering the contents of the “CS2 – Risk Modelling and Survival Analysis Core Principles” subject of the Institute and Faculty of Actuaries. This counts towards the “Foundation Program” of the Australian Actuaries Institute professional curriculum and syllabus.
In particular, ACTL30007 is meant to cover Items 1 and 2 of the CS2 syllabus. This is detailed in the following table, with mapping towards the course modules (and major reference in parentheses; see “Subject Resources” below), as well as subject intended learning outcomes (SLO).
Item 1 – Random variables and distributions for risk modelling #
| CS2 | Subject module (main reference) | SILO |
|---|---|---|
| 1.1 Loss distributions, with and without risk sharing. | Module 3 Individual Claim Size Modelling (MW 3), and | 1, 2, 3, 4 |
| Module 4* Algorithms and Approximations for compound distributions (MW 4) | 6* | |
| 1.1.1 Describe the properties of the statistical distributions that are suitable for modelling individual and aggregate losses. | ||
| 1.1.2 Explain the concepts of excesses (deductibles) and retention limits. | ||
| 1.1.3 Describe the operation of simple forms of proportional and excess of loss reinsurance. | ||
| 1.1.4 Derive the distribution and corresponding moments of the claim amounts paid by the insurer and the reinsurer in the presence of excesses (deductibles) and reinsurance. | ||
| 1.1.5 Estimate the parameters of a failure time or loss distribution when the data is complete, or when it is incomplete, using maximum likelihood and the method of moments. | ||
| 1.1.6 Fit a statistical distribution to a data set and calculate appropriate goodness-of-fit measures. | ||
| 1.2 Compound distributions and their applications in risk modelling. | Module 2 Collective Risk Modelling (MW 2) | 1, 2, 5 |
| Module 4* Algorithms and Approximations for compound distributions (MW 4) | 6* | |
| 1.2.1 Construct models appropriate for short-term insurance contracts in terms of the numbers of claims and the amounts of individual claims. | ||
| 1.2.2 Describe the major simplifying assumptions underlying the models in 1.2.1. | ||
| 1.2.3 Define a compound Poisson distribution and show that the sum of independent random variables, each having a compound Poisson distribution, also has a compound Poisson distribution. | ||
| 1.2.4 Derive the mean, variance and coefficient of skewness for compound binomial, compound Poisson and compound negative binomial random variables. | ||
| 1.2.5 Repeat 1.2.4 for both the insurer and the reinsurer after the operation of simple forms of proportional and excess of loss reinsurance. | ||
| 1.3 Introduction to copulas. | Module 5 Copulas (CS2, Unit 3) | 1, 7 |
| 1.3.1 Describe how a copula can be characterised as a multivariate distribution function that is a function of the marginal distribution functions of its variates, and explain how this allows the marginal distributions to be investigated separately from the dependency between them. | ||
| 1.3.2 Explain the meaning of the terms ‘dependence or concordance’, ‘upper and lower tail dependence’, and state in general terms how tail dependence can be used to help select a copula suitable for modelling particular types of risk. | ||
| 1.3.3 Describe the form and characteristics of the Gaussian copula and the Archimedean family of copulas. | ||
| 1.4 Introduction to extreme value theory. | Module 6 Extreme Value Theory (CS2, Unit 4) | 1, 8 |
| 1.4.1 Recognise extreme value distributions, suitable for modelling the distribution of severity of loss and their relationships. | ||
| 1.4.2 Calculate various measures of tail weight and interpret the results to compare the tail weights. |
\(*\) Module 4 (SILO 6) covers associated recursive methods and approximations. While all materials are provided as part of this subject, some are neither taught nor assessed for lack of time. Note these are not part of the syllabus.
Item 2 – Time series #
| CS2 | Subject module | SILO |
|---|---|---|
| 2.1 Concepts underlying time series models. | Module 7 Characteristics of Time Series (TS 1.1-1.5) | 1, 9 |
| Module 8 Time Series Regression and Exploratory Data Analysis (TS 2) | ||
| Module 9 Time Series Models (TS 3.1, 3.3, 3.6, 3.9, 5.6) | ||
| 2.1.1 Explain the concept and general properties of stationary, I(0), and integrated, I(1), univariate time series. | ||
| 2.1.2 Explain the concept of a stationary random series. | ||
| 2.1.3 Explain the concept of a filter applied to a stationary random series. | ||
| 2.1.4 Know the notation for backwards shift operator, backwards difference operator and the concept of roots of the characteristic equation of time series. | ||
| 2.1.5 Explain the concepts and basic properties of Autoregressive (AR), Moving Average (MA), Autoregressive Moving Average (ARMA) and Autoregressive Integrated Moving Average (ARIMA) time series. | ||
| 2.1.6 Explain the concept and properties of discrete random walks and random walks with normally distributed increments, both with and without drift. | ||
| 2.1.7 Explain the basic concept of a multivariate autoregressive model. | ||
| 2.1.8 Explain the concept of cointegrated time series. | ||
| 2.1.9 Show that certain univariate time series models have the Markov property and describe how to rearrange a univariate time series model as a multivariate Markov model. | ||
| 2.2 Applications of time series models. | Module 10 Estimation and Forecasting (TS 3.3, 3.5, 3.7) | 1, 9 |
| 2.2.1 Outline the processes of identification, estimation and diagnosis of a time series, the criteria for choosing between models and the diagnostic tests that may be applied to the residuals of a time series after estimation. | ||
| 2.2.2 Describe briefly other non-stationary, non-linear time series models. | ||
| 2.2.3 Describe simple applications of a time series model, including random walk, autoregressive and cointegrated models, as applied to security prices and other economic variables. | ||
| 2.2.4 Develop deterministic forecasts from time series data, using simple extrapolation and moving-average models, applying smoothing techniques and seasonal adjustment when appropriate. |
Mapping to the Society of Actuaries Exams #
This subject is one of several subjects covering the contents of the Exam FAM–Fundamentals of Actuarial Mathematics, and several subjects covering the contents of the Exam ASTAM–Advanced Short-Term Actuarial Mathematics.
This counts towards the “Centers for Actuarial Excellence” (CAE) accreditation by the Society of Actuaries (SoA).
Exam FAM–Fundamentals of Actuarial Mathematics #
We cover from the FAM syllabus:
- Item 1: c)-g)
- Item 2: a)-d), h), i)
- Item 3
Exam ASTAM–Advanced Short-Term Actuarial Mathematics #
We cover from the ASTAM syllabus:
- Item 1
- Item 2
- Item 3
- Item 4: a), e)