Module: Financial & Actuarial Models

Latest Module Specifications

Current Academic Year 2025 - 2026

Module Title	Financial & Actuarial Models
Module Code	MTH1001 (ITS: MS349)
Faculty	Mathematical Sciences	School	Science & Health
NFQ level	8	Credit Rating	7.5

Description

This module aims to develop data analysis and modelling techniques for risk management for finance and insurance applications. Classical return and loss distributions will be described and techniques for choosing and fitting distributions to sample data will be presented. Models for aggregate claims data will be developed. Advanced topics in the use of copulas for modelling dependencies between risks and extreme value theory will be introduced. Exploratory data analysis and machine learning techniques for Big Data will be examined in the context of risk management. Practical analysis and modelling examples will be provided throughout the course using R.

Learning Outcomes

1. Identify and fit appropriate return and loss distributions using R.
2. Explain the use of reinsurance in risk management for insurance companies.
3. Develop risk models for aggregate claims.
4. Understand, fit, and forecast ARIMA time series models.
5. Use of copulas in modelling dependencies between risks.
6. Apply extreme value theory to insurance problems.
7. Understand CAPM and multifactor asset pricing models. Regressions and related tests.
8. Principal component analysis. Yield curve and futures modelling.
9. Apply simple machine learning techniques to big data for the insurance industry using R.

*Type*	*Hours*	*Description*
Workload	Full time hours per semester
Lecture	24	Classes
Laboratory	24	Practical sessions.
Independent Study	140	Independent work
Total Workload: 188

Section Breakdown
CRN	10063	Part of Term	Semester 1
Coursework	0%	Examination Weight	0%
Grade Scale	40PASS	Pass Both Elements	Y
Resit Category	RC1	Best Mark	N
Module Co-ordinator	Paolo Guasoni	Module Teacher

Type	Description	% of total	Assessment Date
Assessment Breakdown
In Class Test	Laboratory practical test	25%	n/a
Formal Examination	Final Exam	75%	End-of-Semester

Reassessment Requirement Type
Resit arrangements are explained by the following categories; RC1: A resit is available for both^* components of the module. RC2: No resit is available for a 100% coursework module. RC3: No resit is available for the coursework component where there is a coursework and summative examination element. ^* ‘Both’ is used in the context of the module having a coursework/summative examination split; where the module is 100% coursework, there will also be a resit of the assessment

Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml

Indicative Content and Learning Activities

Return and Loss Distributions
Risk management; classical return and loss distributions; proportional and excess of loss reinsurance; statistical tests; model fitting and checking.

Aggregate Claims Modelling
Aggregate loss distributions; Compound Poisson distribution; allowance for reinsurance.

Time Series Models
ARIMA models, fitting, and forecasting.

Copulas
Multivariate distributions; properties of copulas; concordance measures – Kendall’s tau and Spearman’s rho; Copula selection; Gaussian copula; Archimedean copula family; Elliptical copulas.

Extreme Value Theory
Extreme value distributions; block maxima; exceedances; tail weights.

Asset Pricing Models
CAPM and multifactor models; tests of linear models; multivariate regressions and factors.

Machine Learning
Supervised and unsupervised machine learning algorithms; principal component analysis; regression and classification; applications of machine learning techniques in R.

Indicative Reading List

Books:
None

Articles:
None

Other Resources

None