MODULES

Aim
The aim of the Advanced Actuarial Mathematics course is to build on the fundamentals of the mathematics of finance and life contingencies and to provide a sound undertaking of the application of the actuarial philosophy and the actuarial scientific method to file insurance.

Objectives
On completion of the module the trainee actuary will be able to:

• show an understanding of simple stochastic interest rate models,
• analyze compound interest problems and solve an equation of value for the implied rate of interest,
• evaluate the liabilities under a capital redemption contract or annuity certain, in terms of emerging costs and in terms of present values, for the purposes of product pricing and for the purposes of reserving,
• demonstrate how to use a single decrement model to describe the evolution of a population subject to a single decremental factor, both in discrete and continuous form, and with and without selection,
• analyze simple problems of emerging costs using a single decrement model,
• evaluate the liabilities under a simple assurance contract or annuity contract, in terms of emerging costs and in terms of present values for the purposes of product pricing, reserving and the calculation of surrender values,
• demonstrate how the emergence of profit on simple assurance contract or annuity contract depends on the interaction between the pricing basis and the reserving basis,
• analyze problems of emerging costs using single or multiple state pr multiple decrement model,
• calculate the present value and the accumulated value of a stream of payments using a single rate of interest and taking into account the probability of the payments being made according to a single decrement or a multiple state or multiple decrement model,
• analyze problems involving an equation of value taking into account the probability of the payments being made according to a single decrement or a multiple state or multiple decrement model,
• define and use Manchester Unity sickness functions as an alternative method to a multiple state model for analyzing problems involving sickness and discuss the advantages and limitations of the method,
• define and use straightforward functions involving more than one life,
• define and use simple commutation functions suitable for valuing pension fund benefits and contributions;
• apply methods and techniques in sections (h) to (m) to a range of problems,
• carry out a straightforward profit test of a life insurance product.