Course syllabus - Actuarial Mathematics

Objectives

Actuarial mathematics constitutes the mathematical foundation of the insurance business. The stochastic nature of accidents and the length of people s lives make uncertainty an integral part of this business. The course Actuarial Mathematics provides students with essential knowledge and tools required to explore the consequences of uncertainty as well as to solve other mathematical and statistical problems arising in the insurance business. It provides basics in the mathematical techniques which can be used to model and value cash flows dependent on death, survival, or other uncertainties depending on risks. The concepts of risk theory and risk processes are introduced. Various forms of life insurance and their mechanisms are considered. Insurance models, reinsurance contracts, different types of distributions and simulation methods for both claim sizes and claim numbers will be analysed in the framework of non-life insurance.

Learning outcomes

At the end of the course the student is expected to be able to
- describe and calculate compound interests and financial annuities.
- operate with distribution functions and densities of future lifetime, the probabilities of survival/death, and force of mortality, and describe the construction and use of life tables.
- define standard life insurance and annuity contracts (including the contracts with variable benefits) and to calculate the mean and variance of the present value of benefit payments under each of the standard contracts.
- define and calculate net level premiums and evaluate net premium reserves in respect of the standard contracts.
- describe and analyse claim flows (number of claims, claim amounts, aggregate claims amount, operate with claim size distributions, describe large and catastrophic claims, estimate and approximate characteristics of aggregate claim distributions, and calculate premiums).
- use Cramèr-Lundberg's and other approximations for ruin probabilities.
- describe basic models of reinsurance.
- describe methods of stochastic modeling of insurance and reinsurance business.

Course content

Compound interests. Financial annuities. Lifetime distributions. Survival function. Life tables. Whole-life and term insurance. Pure endowments. Endowments. Life annuities. Net premiums. Net premium reserves. Claim flow (number of claims, claim amounts, aggregate claims amount). Claim number and claim size distributions (Poisson, mixed Poisson, Pareto, etc.). Premiums. Collective risk model. Recursive and approximate calculation of aggregate claims distributions. Ruin probability. Cramèr-Lundberg's and other approximations. Large and catastrophic claims. Reinsurance. Stochastic modelling with applications to (re)insurance.

Tuition

Lectures combined with exercises. Continuous examination of problems/projects combined with written tests. Examination of seminars through oral presentation of written reports.

Specific requirements

At least totally 120 credits in the engineering, natural sciences, business administration or economics areas where Probability 7.5 credits or equivalent is included. In addition Swedish course B/Swedish course 3 and English course A/English course 6 are required. For courses given entirely in English exemption is made from the requirement in Swedish course B/Swedish course 3.

Examination

Continuous examination/project (PRO1), 4.5 credits, marks Pass (G) or Pass with distinction (VG)
Seminars (SEM1), 3 credits, marks Pass (G)

A student who has a certificate from MDU regarding a disability has the opportunity to submit a request for supportive measures during written examinations or other forms of examination, in accordance with the Rules and Regulations for Examinations at First-cycle and Second-cycle Level at Mälardalen University (2020/1655). It is the examiner who takes decisions on any supportive measures, based on what kind of certificate is issued, and in that case which measures are to be applied.

Suspicions of attempting to deceive in examinations (cheating) are reported to the Vice-Chancellor, in accordance with the Higher Education Ordinance, and are examined by the University’s Disciplinary Board. If the Disciplinary Board considers the student to be guilty of a disciplinary offence, the Board will take a decision on disciplinary action, which will be a warning or suspension.

Grade

Three-grade scale