Provide a solid grounding in the subject of the analysis of life assurance, life annuities, pension contracts, multiple-state models, life contingencies for multiple-life and profit testing.

Provide an introduction to mathematical methodology and methods for managing the risk in life insurance.

Analyse problems of pricing, valuation and reserving in relation to contracts involving multiple lives and complex insurance products.

Prepare the students to sit for the exams of CM1 subjects of the Institute and Faculty of Actuaries.

Be confident in solving life insurance problems using R programming language.

(LO1) Analyse the concept (and the mathematical assumptions) of the joint future lifetime random variables in continuous and discrete time.

(LO2) Be able to define the probabilities of either or both two lives, explain these types of probabilities and the force of mortality intuitively, and be able to calculate the different types of probabilities in multiple state models both in theoretical and numerical examples.

(LO3) Understand, define and derive the expected present values of different types of life assurances and life annuities. Be able to calculate the expected present values of cashflows for pricing and reserving of life assurances and life annuities in theoretical and numerical examples.

(LO4) Demonstrate an understanding of different insurance contracts and pension products. Be able to calculate present values and solve questions in pension-type examples. Project cashflows to profit test life insurance contracts.

(LO5) Be familiar with R software and be able to use it in the context of life insurance.

(S1) Be able to model and solve problems arising from certain life contingency examples.

(S2) Use R to calculate the expected present values of different types of assurances numerically.

a) Revision of Life insurance I. Survival models, life tables, insurance benefits, premium calculation and reserves.

b) Multiple state models (Markov models). The death-alive model, term insurance with increasing benefit on accident death, the permanent disability model, the disability income insurance model, the joint life and last survivor model, assumptions of the models, probabilities based on intensities using Kolmogorov’s equations, transition intensities based on probabilities, numerical evaluation of probabilities, valuation of insurance products and Thiele’s differential equation.

c) Multiple-life actuarial functions. Joint life survival functions for the joint future lifetimes, probabilities of death and survival of either or both two lives, relations between the joint survival probabilities and the corresponding probabilities of the one life, joint life and last survivor assurance and annuity functions, expected present value, extension to consid eration of continuous and monthly frequencies, joint life table functions, numerical applications.

d) Pension mathematics. Multiple decrement models, construction and use of a multiple decrement service table for pension calculation, pension plans, defined benefit plans, defined contribution plans, replacement ratios and salary scale functions.

e) Emerging costs for different contract types and pensions. With-profit insurance contracts, Unit-linked contracts and disability long-term contracts, the profit test of annual premium contracts, the profit vector, the net present value, the profit signature, the profit margin, and the profit test to price a produce/determine reserves by zeroising.