75319 - Actuarial Mathematics

Learning outcomes

At the end of the course the student masters the main concepts of actuarial mathematics, starting with the main measures of risk analysis. The student will be exposed to the main techniques of evaluation of portfolios of losses for the analysis of portfolios of catastrophe insurance policies.

Course contents

The course is divided into three parts.

- Non-Life insurance

• The collective risk model: Lundberg's model
• Models for claim counts: the binomial distribution, the Poisson distribution, the mixed Poisson distribution, the ngative binomial distribution.
• Models for claim sizes: light and heavy tailed distributions, subexponential distributions (Gamma, Weibull, Log-normal, Log-gamma, Pareto distributions)
• Compound distributions for portfolios of losses: Panjer recursion scheme, normal approximation, approximation for subexponential claims 
• Classical premium calculation principle
  
  

- Life Insurance

• Survival models: the forse of mortality, mortality laws, life tables and fractional age assumptions, select survival models
  
• Insurance contracts: whole life insurance, term insurance, pure endowment, endowment insurance, deferred insurance benefits
• Annuities: annual life annuities (whole life annuity-due, term annuity-due, whole life immediate annuity, term immediate annuity), annuity payable continuously (whole life and term cases), annuities payable 1/m-thly (whole life and term cases), deferred annuities
• Premium calculation: the equivalence principle, percentile premium principle

- Ruin Theory

• Renewal processes
• Lundberg ruin theory

Readings/Bibliography

• Lecture Notes provided by the teacher on each of the three topics of the course (available on Virtuale)
• List of exercises (available on Virtuale)

For further readings it is suggested to refer to:

• M.V. Wuthrich: Non-Life Insurance: Mathematics & Statistics", https://papers.ssrn.com/sol3/papers.cfm?abstract id=2319328
• T. Mikosch (2009): "Non-life Insurance Mathematics", Springer
• D.C.M. Dickson, M.R. Hardy and H.R. Waters: "Actuarial Mathematics for Life Contingent Risks", Cambridge University Press
• A. Olivieri, E. Pitacco: "Introduction to Insurance Mathematics", Springer

Teaching methods

Traditional type classes are given using a tablet. The notes written by the teacher on the tablet are uploaded on Virtuale and so made available to students.

Every week a list of exercises is assigned to students in order to apply the theory presented and weekly tutorial classes are scheduled to correct and discuss exercises solutions.

A mock written exam is provided at the end of the course to be solved at home and then corrected by the tutor.

Some examples of past written exams are available on Virtuale.

Assessment methods

The exam consists in a mandatory written exam and in a mandatory oral exam.

There is no distinction between attending and non-attending students.

The written exam consists of two exercises  (one on non-life insurance and one on life insurance) and it is designed to ascertain students capability to correctly model and evaluate the insurance contracts proposed and to correctly manage the related theoretical tools. It is a "closed book" examination and no books or notes can be consulted. The written test lasts 90 minutes. The maximum score obtainable in the written exam is 33 and it is splitted almast equally into the two exercises (some few points of difference are in some cases justified by the particular exercises specifications).  Students with a score greater or equal to 15 out of 33 are admitted to the mandatory oral exam.

 

The oral exam consists of three theoretical questions each on one of the topics of the course (non-life insurance, life insurance, ruin theory) and it lasts about 10-15 minutes. The aim of the oral exam is to ascertain the knowledge of the concepts introduced, the proofs of the mathematical results presented and applied, the correctness of the technical language.

The oral exam is scheduled or the day after the written exam or in the same day and students that are admitted to the oral examcan decide to give the oral exam in the same session or in one of the next sessions scheduled in the academic year (that is by September session). 

Students may freely decide to repeat the written test, even if the score obtained is sufficient to be admitted to the oral exam, and they may refuse the final grade after the oral exam: in this case they must also repeat the written test.

 

Teaching tools

Classes are conducted using a tablet.


The Unibo Virtual e-learning platform is used to share with students the teaching material that includes:


-Single classes notes from the tablet

-Lectures notes on the macro-topics of the course

- Weekly lists ofhomeworks

- A mock test with solution

- Examples of past exam tests

- Solutions and corrections of the exam tests taken during the year

Office hours

See the website of Sabrina Mulinacci