Project III

Actuarial Mathematics

Frank Coolen

Description

Actuarial mathematics considers risks in insurance, finance, and pension industries. It combines a range of basic mathematical methods, mainly from mathematical finance, probability and statistics. It involves calculating the present value of future contingent events, such as mortality or, in general, financial losses, using tools like deterministic and stochastic models, life tables, and interest theory. This project will introduce students to basic theory of actuarial mathematics, in particular considering life insurance, followed by a range of possible topics to consider in more detail.

Group Project

The group project will focus on basic theory of life insurance. Topics that will be studied are:

  • Mathematics of compound interest, including perpetuities and annuities
  • Lifetime models, including life tables and parametric models
  • Life insurance, including a variety of policies
  • Computing premiums and reserves

Mode of Operation and Evidence of Learning for the group project

The project will revolve around learning through reading with focus on the underlying theory, mathematical rigour, and the development of deep conceptual understanding. Students will demonstrate their understanding by solving relevant problems, exploring examples and theoretical applications of the material, and clearly communicating it in both written and oral formats.

Individual Project

The individual project will build on the knowledge gained in the group project and will explore additional advanced topics. Examples of topics you will be able to investigate are:
  • Life insurance portfolios
  • Linking life insurance benefits to investment performance
  • Pension plans
  • Non-life insurance

Mode of Operation and Evidence of Learning for the individual project

The project will revolve around learning through reading with focus on the underlying theory, mathematical rigour, and the development of deep conceptual understanding. Students will demonstrate their understanding by solving relevant problems, exploring examples and theoretical applications of the material, and clearly communicating it in both written and oral formats.

Prerequisites

Probability I and Statistics I

Additional information

If you have any questions about this project, email me at Frank Coolen

Resources

There are many suitable books on Actuarial Mathematics, most of which provide suitable introductions to the theory. One challenge is to get to grips with many different notations used in the field, from this perspective it is best to use one book as main resource. I recommend Introduction to Insurance Mathematics by Olivieri and Pitacco (2nd Edition, 2015, Springer).