The word actuary derives from the Latin actuarius, who was the business manager of the Senate of Ancient Rome. It was applied to a mathematician of an insurance company in 1775 in the Equitable Life Insurance Society of London.
Actuarial science
This provides a structured and rigid approach to modelling and analysing uncertain outcomes of events that may impose or imply losses or liabilities upon individuals or organisations.
Given that uncertainty is a main characteristic of actuarial events, it follows that probability must be the cornerstone in the structure of actuarial science. Probability in turn rests on pure mathematics.
In order to enable probabilistic modelling of actuarial events to be a realistic and representative description of real-life phenomena, understanding of the “physical nature” of the events under consideration is a basic prerequisite. Pure mathematics and pure probability must therefore be supplemented with and supported by the sciences that deal with such “physical nature” understanding of actuarial events.
Actuarial practice
The main practice areas for actuaries can broadly be divided into: life insurance and pensions; general/nonlife insurance; and financial risk.
There are certain functions in which actuaries have a statutory role. Evaluation of reserves in life and general insurance and in pension funds is an actuarial process, and it is a requirement under the legislation in most countries that this evaluation is undertaken and certified by an appointed actuary. The role of an appointed actuary has long traditions in life insurance and in pension funds. A similar requirement has been introduced by an increasing number of countries since the early 1990s.
The involvement of an actuary can be required as a matter of substance in other functions. Then there are functions where actuarial qualifications are neither a formal nor a substantial requirement, but where actuarial qualifications are perceived to be a necessity.
Life insurance and pensions
Assessing and controlling the risk of life insurance and pension undertakings is the origin of actuarial practice and the actuarial profession. The success in managing this risk comprises the following:
•understanding lifetime as a stochastic phenomena, and modelling it within a probabilistic framework;
•evaluating the diversifying effect of aggregating lifetime of several individuals into one portfolio;
•estimating individual death and survival probabilities.
By analysing historic data and projecting future trends, life insurance actuaries constantly maintain both first-order and second-order bases. Premium and premium reserve valuation tariffs and systems are built on the first-order basis. Over time emerging surplus is evaluated and analysed by source, and in due course reverted as policyhold¬ers’ bonus.
General insurance
Over the years actuaries have attained a growing importance in the running of the nonlife insurance operations. The basis for the insurance industry is to accept economic risks. An insurance contract may give rise to claims. Both the number of claims and their sizes are unknown to the company. Thus insurance involves uncertainty and here is where the actuaries have their prerogative; they are experts in insurance mathematics and statistics.
Finance
Financial risk has grown to become a relatively new area for actuaries. Those who practice here are called “actuaries of the third kind”.
It is different from ordinary insurance risk in that increasing the size of a portfolio does not in itself provide a diversification effect. For actuaries it has been a disappointing that the law of large numbers does not come into assistance.
The most fundamental and innovative result in the theory of financial risk/mathematical finance is probably that risk associated with contingent claims can be eliminated by appropriate portfolio management.
This theory is the cornerstone in a new practice field, called financial engineering. Activities include quantitative modelling and analysis, funds management, interest rate performance measurement, asset allocation, and model-based scenario testing. Actuaries may practice financial engineering in their own right, or they may apply financial engineering as an added dimension to traditional insurance-orientated actuarial work.
A field where traditional actuarial methods and methods relating to financial risk are beautifully aligned is asset liability management (ALM). The overriding objective of ALM is to gain insight into how money is best allocated among given financial assets, in order to fulfill specific obligations represented by a future payment stream. The analysis of the obligation’s payment stream rests on traditional actuarial science, the analysis of the asset allocation problem falls under the umbrella of financial risks, and the blending of the two is a challenge that requires insight into both and the ability to understand and model how financial risk and insurance risk interact. ALM is today a key component in the risk management of insurance providers, pension funds, and other financial institutions.
A new challenge on the horizon is the requirement for insurers to prepare financial reports on a market-based principle, which the International Accounting Standards Board has had under preparation for some time. In order to build and apply models and valuation tools that are consistent with this principle, actuaries will be required to combine traditional actuarial thinking with ideas and methods from economics and finance.
This article is an edited version of an entry in the “Encyclopedia of Quantitative Risk Analysis and Assessment”, Copyright © 2008 John Wiley & Sons Ltd. Used by permission.
