1. Provide asolid grounding in the subject of life contingencies for singleand multiple-life, and in the subject of the analysis of life assurance,life annuities, pension contracts, multi-state models and profit testing.           

2. Provide anintroduction to mathematical methods for managing the risk in life insurance

3. Analyse problems of pricingand reserving in relation to contracts involving one and several lives.      

4. Preparethe students to sit for the exams of CT5 subject of the Institute and Facultyof Actuaries.

Be able to explain, define and analyse the single and jointsurvival functions.

Understand the concept (and themathematical assumptions) of the single and joint future life time randomvariables in continuous and discrete time and monthly. Be able to derive thedistributions and the moment/variance of the joint future lifetimes.

Be able to define the survivals probabilities/death probabilitiesof either or both two lives, explain these types of probabilities and the forceof interest intuitively, be able to calculate the different types of thesurvival/death probabilities in theoretical and numerical examples. 

Understand, define and derive theexpected present values of different types of the life assurances and lifeannuities for joint lives, be able to calculate the expected present values ofthe single life and joint life assurances and life annuities intheoretical and numerical examples.

Survival probabilities  

Survivalprobabilities, the force of mortality, versions of the aforementionedsurvival/death probabilities in terms of the force of mortality, Fractional ageassumptions: the De Moivre, Makeham, Gompertz, Weibull and the exponential law(constant force of mortality). Life tables.

LifeAssurances  for one and two lives

Expectedpresent values if life assurances payable at the moment of death (in continuoustime) and at the end of the year of death (in discrete time) for the followingcases: term, whole life, endowment, pure endowment, deferred, term and deferredand their com binations, relations between discrete and continuous timeassurances, increasing and decreasing life assurances, life assurances forvariable insurance benefits, basic monthly life assurances, recursive equationfor the expected present value of different types of life assurances.

Lifeannuities for one and two lives

Introductionto annuities, expected present values (in discrete and continuous time) of anwhole life annuity due/immediate, term annuity due/ immediate, deferred termannuity due/ immediate, whole life annuity, term annuity deferred continuouslypayable, pure endowment, temporary annuity, relations between different typesof annuities, relations between annuities and life assurances in discrete andcontinuous time, fractional annuities, guaranteed annuities, increasing(arithmetically / geometrically) annui ties.

Netand gross premium calculation  for one and two lives

Thepresent value of the future loss random variable, the equivalence principle(net premiums), premiums for different types of annuities (payable monthly,semi-quarterly, annually and continuously), prospective and retroprospectivereserves.

Mortalityprofit, profit contracts, surrender values, net premiums and reserves forcontracts with benefits/profit contracts, gross premiums using the equivalenceprinciple for different types of benefits.

Emergency costs for all contracttypes and pensions

Unit-linke d contracts and disability long-term contracts, profit testannual premium contracts, the profit vector, the net present value, the profitsignature, the profit margin, the profit test to price a product/determinereserves, construction and use of a multiple decrement service table forpension calculation, extension of the above techniques to calculate expectedcash flows contingent risk other than human lives. 

Selection and heterogeneity

Principal factors which contribute tothe variation in mortality and morbidity by region and according to:occupation, nutrition, housing, geography, education.   Examples of main forms of selection: temporary or initialselection, class selection, time selection, spurious selection, adverseselection, necessity of different mortality tables for different classes oflives, the theoretical basis of the use of risk classification in lifeinsurance, definitions of the terms: crude index, direct/indirect standardization,standardized mortality/ morbidity rate, SMR.