Actuarial science

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Actuarial science applies mathematical and statistical methods to finance and insurance, particularly to the assessment of risk. Actuaries are professionals who are qualified in this field through highly competitive examinations and experience.

Actuarial science includes a number of interrelating disciplines, including probability and statistics, finance, and economics. Historically, actuarial science used deterministic models in the construction of tables and premiums. The science has gone through revolutionary changes during the last 30 years due to the proliferation of high speed computers and the synergy of stochastic actuarial models with modern financial theory (Frees 1990).

In traditional life insurance, actuarial science focuses on the analysis of mortality, the production of life tables, and the application of compound interest to produce life insurance, annuities and endowment policies. Contempory life insurance programs have been extended to include credit and morgage insurance, key man insurance for small businesses, long term care insurance and medical savings accounts (Hsiao 2001).

In health insurance and corporate benefit programs in the USA, and social insurance, actuarial science focuses on the analyses of rates of disability, morbidity, mortality, fertility and other contingencies. The effects of the geographical distribution of the utilization of medical services and procedures, and the utilization of drugs and therapies, is also of great importance. These factors underly the development of the Resource-Base Relative Value Scale (RBRVS) at Harvard in a multi-disciplined study. (Hsiao 1988) Actuarial science also aids in the design of benefit structures, reimbursement standards, and the effects of proposed governemnt standards on the cost of healthcare (cf. CHBRP 2004).

In the pension industry, actuarial methods are used to measure the costs of alternative strategies with regard to the design, maintenance or redesign of pension plans. The strategies are greatly influenced by collective bargaining; the employer's old, new and foreign competitors; the changing demographics of the workforce; changes in the internal revenue code; changes in the attitude of the internal revenue service regarding the calculation of surpluses; and equally importantly, both the short and long term financial and economic trends. It is common with mergers and acquisitions that several pension plans have to be combined or at least administered on an equitable basis. When benefit changes occur, old and new benefit plans have to be blended, satisfying the demands of political correctness and various government discrimination test calculations, and providing employees and retirees with understandle choices and transition paths. Benefit plans liabilities have to be properly valued, reflecting both earned benefits for past service, and the benefits for future service. Finally, funding schemes have to be developed that are manageable and satify the Financial Accounting Standards Board (FASB).

In social welfare programs, the Office of the Chief Actuary (OCACT), Social Security Administration plans and directs a program of actuarial estimates and analyses relating to SSA-administered retirement, survivors and disability insurance programs and to proposed changes in those programs. It evaluates operations of the Federal Old-Age and Survivors Insurance Trust Fund and the Federal Disability Insurance Trust Fund, conducts studies of program financing, performs actuarial and demographic research on social insurance and related program issues involving mortality, morbidity, utilization, retirement, disability, survivorship, marriage, unemployment, poverty, old age, families with children, etc., and projects future workloads. In addition, the Office is charged with conducting cost analyses relating to the Supplemental Security Income (SSI) program, a general-revenue financed, means-tested program for low-income aged, blind and disabled people. The Office provides technical and consultative services to the Commissioner, to the Board of Trustees of the Social Security Trust Funds, and its staff appears before Congressional Committees to provide expert testimony on the actuarial aspects of Social Security issues.

In the property and casulaty insurance fields, which protect against losses like those caused by hurricanes as well as automobile accidents, actuarial science tries to forecast aggregate losses to persons and property.

In reinsurance, actuarial science attempts to predict the behavior of large blocks of policies affecting a particular cedant company. This can be very different from cedant to cedant, as it depends strongly on the insureds claims handling and underwriting abilities.

Many universities have undergraduate and graduate degree programs in actuarial science.

Development

Pre-formalization

In the ancient world there was no room for the sick, suffering, disabled, aged, or the poor—it was not part of the cultural consciousness of societies (Perkins 1995). Early methods of protection involved charity; religious organizations or neighbors would collect for the destitute and needy. By the middle of the third century, 1,500 suffering people were being supported by charitable operations in Rome (Perkins 1995). Charitable protection is still an active form of support to this very day (Tong 2006). However, receiving charity is uncertain and is often accompanied by social stigma. Elementary mutual aid agreements and pensions did arise in antiquity (Thucydides c. 431BCE). Early in the Roman empire, associations were formed to meet the expenses of burial, cremation, and monuments—precusors to burial insurance and friendly societies. A small sum was paid into a communal fund on a weekly basis, and upon the death of a member, the fund would cover the expenses of rites and burial. These societies sometimes sold shares in the building of columbāria, or burial vaults, owned by the fund—the precursor to mutual insurance companies (Johnston 1903, §475–§476). Other early examples of mutual surety and assurance pacts can be traced back to various forms of fellowship within the Saxon clans of England and their Germanic forbears, and to Celtic society (Loan 1992). However, many of these earlier forms of surety and aid would often fail due to lack of understanding and knowledge (Faculty and Institute of Actuaries 2004).

Initial development

The seventeenth century was a period of extraordinary advances in mathematics in Germany, France and England. At the same time there was a rapidly growing desire and need to place the valuation of personal risk on a more scientific basis. Independently from each other, compound interest was studied and probability theory emerged as a well understood mathematical discipline. Another important advance came in 1662 from a London draper named John Graunt, who showed that there were predictable patterns of longevity and death in a defined group, or cohort, of people, despite the uncertainty about the future longevity or mortality of any one individual person. This study became the basis for the original life table. It was now possible set up an insurance scheme to provide life insurance or pensions for a group of people, and to calculate with some degree of accuracy, how much each person in the group should contribute to a common fund assumed to earn a fixed rate of interest. The first person to demonstrate publicly how this could be done was Edmond Halley. In addition to constructing his own life table, Halley demonstrated a method of using his life table to calculate the premium or amount of money someone of a given age should pay to purchase a life-annuity (Halley 1693).

Early actuaries

James Dodson’s pioneering work on the level premium system led to the formation of the Society for Equitable Assurances on Lives and Survivorship (now commonly known as Equitable Life) in London in 1762. The company still exists, though it has run into difficulties recently. This was the first life insurance company to use premium rates which were calculated scientifically for long-term life policies. Many other life insurance companies and pension funds were created over the following 200 years. It was the Society for Equitable Assurances which first used the term ‘actuary’ for its chief executive officer in 1762. Previously, the use of the term had been restricted to an official who recorded the decisions, or ‘acts’, of ecclesiastical courts (Faculty and Institute of Actuaries 2004). Other companies which did not originally use such mathematical and scientific methods, most often failed, or were forced to adopt the methods pioneered by Equitable (Bühlmann 1997 p. 166).

Effects of technology

In the eighteenth and nineteenth centuries, computational complexity was limited to manual calculations. The actual calculations required to compute fair insurance premiums are rather complex. The actuaries of that time developed methods to construct easily-used tables, using sophisticated approximations called commutation functions, to facilitate timely, accurate, manual calculations of premiums (Slud 2006). Over time, actuarial organizations were founded to support and further both actuaries and actuarial science, and to protect the public interest by ensuring competency and ethical standards (Hickman 2004 p. 4). However, calculations remained cumbersome, and actuarial shortcuts were commonplace. Non-life actuaries followed in the footsteps of their life compatriots in the early twentieth century. The 1920 revision to workers compensation rates took over two months of around-the-clock work by day and night teams of actuaries (Michelbacher 1920 p. 224, 230). In the 1930s and 1940s, however, the rigorous mathematical foundations for stochastic processes were developed (Bühlmann 1997 p. 168). Actuaries could now begin to forecast losses using models of random events, instead of the deterministic methods they had been constrained to in the past. The introduction and development of the computer industry further revolutionized the actuarial profession. From pencil-and-paper to punchcards to current high-speed devices, the modeling and forecasting ability of the actuary has grown exponentially, and actuaries needed to adjust to this new world (MacGinnitie 1980 p.50-51).

Actuarial science and modern financial economics

Some aspects of traditional actuarial science are not aligned with modern financial economics. Pension actuaries have been challenged by financial economists regarding funding and investment strategies. There are two reasons for the divergence of actuarial and financial economic practices. The first deals with the shear complexity of calculations, and the second with the heavy burden of regulations resulting from the Armstrong investigation of 1905, the Glass-Steagal Act of 1932, the adoption of the Mandatory Security Valuation Reserve by the National Association of Insurance Commissioners; the latter law cushioned market fluctuations. Finally pensions valuations and funding must comply with the Financial Accounting Standards Board, (FASB) in the USA and Canada. The regulatory burden led to a separation of powers regarding the management and valuation of assets and liabilities.

Historically, much of the foundation of actuarial theory predated modern financial theory. In the early twentieth century, actuaries were developing many techniques that can be found in modern financial theory, but for various historical reasons, these developments did not achieve much recognition (Whelan 2002). As a result, actuarial science developed along a different path, becoming more reliant on assumptions, as opposed to the arbitrage-free risk-neutral valuation concepts used in modern finance. The divergence is not related to the use of historical data and statistical projections of liability cash flows, but is instead caused by the manner in which traditional actuarial methods apply market data with those numbers. For example, one traditional actuarial method suggests that changing the asset allocation mix of investments can change the value of liabilities and assets (by changing the discount rate assumption). This concept is inconsistent with financial economics.

The potential of modern financial economics theory to complement existing actuarial science was recognized by actuaries in the mid-twentieth century (Bühlmann 1997 p. 169–171). In the late 1980s and early 1990s, there was a distinct effort for actuaries to combine financial theory and stochastic methods into their established models. (D’arcy 1989). Ideas from financial economics became increasingly influential in actuarial thinking, and actuarial science has started to embrace more sophisticated mathematical modelling of finance (The Economist 2006). Today, the profession, both in practice and in the educational syllabi of many actuarial organizations, is cognizant of the need to reflect the combined approach of tables, loss models, stochastic methods, and financial theory (Feldblum 2001 p. 8–9). However, assumption-dependent concepts are still widely used (such as the setting of the discount rate assumption as mentioned earlier), particularly in North America.

Product design adds another dimension to the debate. Financial economists argue that pension benefits are bond-like and should not be funded with equity investments without reflecting the risks of not achieving expected returns. But some pension products do reflect the risks of unexpected returns. In some cases, the pension beneficiary assumes the risk, or the employer assumes the risk. The current debate now seems to be focusing on four principals. 1. financial models should be free of arbitrage; 2. assets and liabilities with identical cash flows should have the same price. This, of course, is at odds with FASB. 3. The value of an asset is independent of its financing. 4. the final issue deals with how pension assets should be invested. Essentially, financial economics state that pension assets should not be invested in equities for a variety of theoretical and practical reasons. (Moriarty 2006).

See also

References

Works Cited

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