Provide a solid grounding in the subject of life contingencies for single life, and in the subject of the analysis of life assurance and life annuities, including pension contracts.

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

Develop skills of calculating the premium for a certain life insurance contract, including allowance for expenses and profits.

Prepare the students adequately and to develop their skills in order to be ready to sit for the exams of CM1 subject of the Institute and Faculty of Actuaries.

(LO1) Compute and approximate survival/death probabilities and construct life tables given a select or ultimate mortality model for a single life.

(LO2) Give summation or integral expressions and evaluate them, including using backward recursive algorithms, for expected present values of annuities and assurances and to provide explanations for the relative values of these objects.

(LO3) Derive or explain relationships between various probabilities or expected present values.

(LO4) Provide expressions for present values associated with life insurance policies and explain how they depend on the (random) lifetime of the life.

(LO5) Define, interpret and use actuarial notation for life insurance objects.

(LO6) Derive expressions for net and gross premiums associated with life insurance policies and to explain and interpret the (sign of the) value of the net/gross premium, reserves and mortality profit and how it depends on the specifications of the policy.

(LO7) Use Excel or R to implement the methods for computing various quantities of interest in life insurance and visualise and interpret the output.

(a) Review of Survival models:

The future lifetime random variable in continuous time, the future lifetime random variable in discrete time, the 1/m future lifetime random variable, moments and distributions of the future lifetimes, the survival function.

(b) Survival probabilities:

Survival probabilities, the force of mortality, versions of the aforementioned survival/death probabilities in terms of the force of mortality, Fractional age assumptions

(c) Life Assurances:

Introduction to contracts of life assurances, expected present values if life assurances payable at the moment of death (in continuous time) and at the end of the year of death (in discrete time) for the following cases: term, whole life, endowment, pure endowment, deferred, term and deferred and their combinations, relations between discrete and continuous time assurances, increasing and decreasing life assurances, life assurances for variable insurance benefits, basic monthly life ass urances, recursive equation for the expected present value of different types of life assurances.

(d) Life annuities:

Introduction to annuities, expected present values (in discrete and continuous time) of an whole life annuity due/immediate, term annuity due/ immediate, deferred term annuity due/ immediate, whole life annuity, term annuity deferred continuously payable, pure endowment, temporary annuity, relations between different types of annuities, relations between annuities and life assurances in discrete and continuous time, fractional annuities, guaranteed annuities, increasing (arithmetically / geometrically) annuities.

(e) Life tables:

Introduction to life tables, the life table functions (select and ultimate). Relations between the life functions and the variables defined in (a).

(f) Net premium calculation and policy values:

The present value of the future loss random variable, the equivalence principle (net premiums), premiums for differ ent types of annuities (payable monthly, semi-quarterly, annually and continuously), prospective and retroprospective reserves.

(g) Benefits, bonuses and expenses:

Mortality profit, profit contracts, surrender values, reserves for contracts with benefits/profit contracts, gross premiums using the equivalence principle for different types of benefits.