Dr Luciano Campi COL.7.10

This course is compulsory on the BSc in Actuarial Science. This course is available on the BSc in Business Mathematics and Statistics and BSc in Statistics with Finance. This course is not available as an outside option nor to General Course students.

Students must have completed Probability, Distribution Theory and Inference (ST202) and Survival Models (ST227).

An introduction to the theory and techniques of life insurance and pensions. Standard single life insurance products; endowments, annuities, and assurances. Extensions to multi-state policies and general benefits and premiums; two lives and more general multi-life functions including the joint life status and last survivor status, the multiple decrements model (competing risks), and the disability model, level and variable payments including increasing and decreasing assurances and annuities. Discrete and continuous time payments. Aggregate and select intensities. Actuarial notation for life contingencies and expected present values of standard products. Principles and techniques for determining premiums and reserves. The principle of equivalence. Thiele's differential equation and its generalizations. Variances and higher order moments of present values. Numerical methods. Woolhouse's formula relating present values in continuous and discrete time. Relationships between payments of annuity type and payments of assurance type. Notions of prospective and retrospective reserves and relationships between them. Administration expenses, gross premiums and gross reserves. With-profit contracts, surplus and dividends, various forms of bonus (cash bonus, terminal bonus, added benefits), interest rate guarantees, unit-linked insurance, defined benefits, defined contributions, salary-related benefits. Techniques for assessing profitability. Elements of population theory applied to life insurance. Heterogeneity, selection phenomena; intensities dependent on policy duration and state duration. Risk classification.

20 hours of lectures and 10 hours of lectures in the MT. 10 hours of lectures and 10 hours of seminars in the LT.

Compulsory written answers to two sets of problems.

R Norberg, Basic Life Insurance Mathematics; The Institute of Actuaries, Core reading Subject CT5

Exam (100%, duration: 3 hours) in the main exam period.