This subject arises through a fusion of compound interest theory with probability theory, and provides the mathematical framework necessary for analysing such contracts, which are essentially long term financial transactions in which the various cash flows at different times are contingent on the death (life assurance) or survival (life annuities) of one or more specified human lives. Having developed this framework, we can address issues such as how to determine the premium that should be charged for a certain life assurance contract, including allowance for expenses and/or profit, and how to determine the value that should be represented in the balance sheet of a life assurance company in respect of the policies that it has sold. These examples reflect the two main traditional areas of actuarial activity within a life assurance company: pricing and reserving.
The module begins with an examination of the various factors that affect mortality, and of how risk classification may be used to address the heterogeneity within a given population. Next, probabilities of survival and death are introduced, and it is shown how these may be represented within and extracted from life tables. Compound interest theory is then combined with such probabilities to analyse and evaluate both life assurance benefits and life annuity benefits. With the relevant theory fully developed, the module then becomes somewhat more applied. Premium calculation is explored in detail first, followed by the determination and application of reserves, and, in both areas, the theory is applied to quite realistic and complex problems. Finally, the alternative perspective of cash-flow analysis, or profit-testing, is introduced and applied to assess the emergence of profit from, and overall profitability of, a life contract.
This module is a pre-requisites for MATH6130