Risk Analysis

Code:

2MDA16

Acronym:

AR

Keywords
Classification	Keyword
OFICIAL	Statistics

Instance: 2021/2022 - 2S

Active?	Yes
Course/CS Responsible:	Master in Modeling, Data Analysis and Decision Support Systems

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
MADSAD	26	Official Syllabus - after 2020-2021	1	-	6	42	162

Teaching language

English

Objectives

The main goal of this subject is to acquire special competences in actuarial science for which the main methodologies used regard the Utility Theory and the Risk Theory. 

 

Learning outcomes and competences

The student should learn concepts of Utility Theory and Insurance and be able to use the techniques associated to the modeling of individual and collective risk for a single and extended period.

Working method

Presencial

Program

1. UTILITY THEORY AND INSURANCE
1.1. Notion of utility function
1.2. Elements of Insurance
1.3. Insurance premium
1.4. Jensen's inequalities
1.5. Basic utility functions

2. INDIVIDUAL RISK MODELS FOR A SHORT TERM
2.1. Basic notions
2.2. Models for individual claim amounts
2.3. Distribution of the aggregate claims
2.3.1. Distribution of the sum of independent random variables
2.3.2. Approximations for the distribution of the sum of independent random variables. Central Limit Theorem
2.3.3. Applications to Insurance

3. COLLECTIVE RISK MODELS FOR A SINGLE PERIOD
3.1. Notion of collective risk model for a single period
3.2. The distribution of aggregate claims
3.3. Frequency distribution
3.4. Severity distribution
3.5. Compound Poisson distribution for the aggregate claims
3.6. Panjer’s recursive formulas
3.7. Approximations for the distribution of aggregate claims

4. COLLECTIVE RISK MODEL OVER AN EXTENDED PERIOD
4.1. Notion of a collective risk model over an extended period
4.2. Distribution of the aggregate claims
4.3. The claim number process and the aggregate claim process

RUIN THEORY
5.1 The surplus process and the ruin probability
5.2 Cramér-Lundberg model
5.3 Adjustment coefficient. Fundamental Theorem of Risk. Lundberg inequality.
5.4 Model in discrete time

 

Mandatory literature

N. L. Bowers Jr, H. U. Gerber, J. C. Hickman, D. Jones e C. J. Nesbitt; Actuarial Mathematics, The Society of Actuaries, Chicago, 1986

Teaching methods and learning activities

The lectures will focus the theoretical aspects of the theory but also include the discussion of exercises.

Evaluation Type

Distributed evaluation without final exam

Assessment Components

Designation	Weight (%)
Exame	75,00
Teste	25,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Estudo autónomo	120,00
Frequência das aulas	42,00
Total:	162,00

Eligibility for exams

All students are admitted to the exam.

Calculation formula of final grade

0.25*(test grade)+0.75*(exam grade)