A view on the evaluation of risk
1.1.1 The role of mathematics
How is evaluation of risk influenced by modern computing? Consider the way we use mathematics, first as a vendor of models of complicated risk processes. These models are usually stochastic. They are in general insurance probability distributions of claim numbers and losses and in life insurance and finance, stochastic processes describing lifecycles and investment returns. Mathematics is from this point of view a language, a way risk is expressed, and it is a language we must master. Otherwise statements of risk cannot be related to reality, it would be impossible to say what conclusions mean in any precise manner and nor could analyses be presented effectively to clients. Actuarial science is in this sense almost untouched by modern computational facilities. The basic concepts and models remain what they were, notwithstanding, of course, the strong growth of risk products throughout the last decades. This development may have had something to do with computers, but not much with computing per se.
However, mathematics is also deductions with precise conclusions derived from precise assumptions through the rules of logic. That is the way mathematics is taught at school and university. It is here that computing enters applied mathematical disciplines like actuarial science. More and more of these deductions are implemented in computers and carried out there. This has been going on for decades. It leans on an endless growth in computing power, a true technological revolution opening up simpler and more general computational methods which require less of users.