Risk theory

Code:

M4059

Acronym:

M4059

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2023/2024 - 1S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Master in Mathematical Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
M:ECAD	2	Study plan since 2021/2022	2	-	6	42	162
M:ENM	13	Official Study Plan since 2023/2024	1	-	6	42	162
			2
M:M	1	Plano Oficial do ano letivo 2021	2	-	6	42	162

Teaching language

Suitable for English-speaking students

Objectives

To introduce the fundamental concepts and principles of risk theory.
To provide a fundamental knowledge of the commonly used stochastic models and techniques in non-life insurance mathematics.

Learning outcomes and competences

To review, develop and integrate knowledge from different areas, with emphasis on probability theory and statistical modeling, necessary for the study of risk theory.

To acquire a sound knowledge of the mathematical theory behind general insurance models, understand the fundamental concepts and principles of risk theory and know how they are used in non-life insurance. To be able to analyze insurance data using adequate statistical methods and the software R.

Students should also develop rigorous communication and written skills, intuition and the ability of statistical modeling. It is also intended that students become familiar with research papers in this area.

Working method

Presencial

Program

 Probabilistic models, fundamental concepts of probability theory and statistics (structured review and development during the course).

 General principles of risk theory, risk models in non-life insurance. Utility and insurance.

 The individual and collective risk models and their characterizations.

Loss modelling. Light-tailed and heavy-tailed distributions. Modelling of the number of claims. The aggregate claims distribution and approximations.

Ruin theory. Risk reserve process, ruin probability (continuous and discrete time models).

Premium principles and risk measures. Reinsurance common treaties and their effects.

Statistical analysis of insurance data, using the software R.

Mandatory literature

Kaas Rob; Modern actuarial risk theory. ISBN: 978-3-642-03407-7
Klugman Stuart A.; Loss models. ISBN: 0-471-23884-8

Complementary Bibliography

Centeno, M. L.; Teoria do Risco na Actividade Seguradora, Celta Editora, 2003
Rolski Tomasz; Stochastic processes for insurance and finance. ISBN: 0-471-95925-1

Teaching methods and learning activities

 Lectures TP where the topics of the syllabus are presented, exercises and related problems are solved and discussed, using the adequate means.

Project work to be developed in team. The discussion of the works is open, all students are encouraged to participate.

Software

R Project

keywords

Physical sciences > Mathematics > Applied mathematics > Actuarial mathematics

Evaluation Type

Distributed evaluation with final exam

Assessment Components

designation	Weight (%)
Exame	60,00
Trabalho prático ou de projeto	40,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	110,00
Frequência das aulas	42,00
Trabalho escrito	10,00
Total:	162,00

Eligibility for exams

Practical assignments/ Project submitted within the fixed  schedules.

Calculation formula of final grade

The evaluation comprehends two components: project (40%) and final exam (60%). A minimum rating of 30% is required in each of the evaluation components.

Classification improvement

The classification obtained in the project component is not subject to improvement and is only valid during the current academic year.