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March 26, 2016
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1 Introduction
actuarial science



Actuarial science is the discipline that applies mathematics|mathematical and statistics|statistical methods to Risk assessment|assess risk in the insurance and finance industries. Actuary|Actuaries are professionals who are qualified in this field through education and experience. In India, the United States, Canada, the United Kingdom, and several other countries, actuaries must demonstrate their competence by passing a series of rigorous professional examinations.

Actuarial science includes a number of interrelating subjects, including probability, mathematics, statistics, finance, economics, and computer programming. 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 union of stochastic actuarial models with modern financial theory .

Many universities have undergraduate and graduate degree programs in actuarial science. In 2010, a study published by job search website CareerCast ranked actuary as the #1 job in the United States (Needleman 2010). The study used five key criteria to rank jobs: environment, income, employment outlook, physical demands and stress. A similar study by U.S. News & World Report in 2006 included actuaries among the 25 Best Professions that it expects will be in great demand in the future (Nemko 2006).

Life insurance, pensions and healthcare

Actuarial science became a formal mathematical discipline in the late 17th century with the increased demand for long-term insurance coverages such as Burial, Life insurance, and Annuities. These long term coverages required that money be set aside to pay future benefits, such as annuity and death benefits many years into the future. This requires estimating future contingent events, such as the rates of mortality by age, as well as the development of mathematical techniques for discounting the value of funds set aside and invested. This led to the development of an important actuarial concept, referred to as the Present value of a future sum. Pensions and healthcare emerged in the early 20th century as a result of collective bargaining. Certain aspects of the actuarial methods for discounting pension funds have come under criticism from modern financial economics.

  • In traditional life insurance, actuarial science focuses on the analysis of mortality rate|mortality, the production of life tables, and the application of interest|compound interest to produce life insurance, annuities and endowment policies. Contemporary life insurance programs have been extended to include credit and mortgage insurance, key man insurance for small businesses, long term care insurance and Medical savings account|health savings accounts .

  • In health insurance, including insurance provided directly by employers, and social insurance, actuarial science focuses on the analysis of rates of disability, morbidity, mortality, fertility and other contingencies. The effects of consumer choice and 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 underlay the development of the Resource-Base Relative Value Scale (RBRVS) at Harvard in a multi-disciplined study. Actuarial science also aids in the design of benefit structures, reimbursement standards, and the effects of proposed government standards on the cost of healthcare .

  • 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 new social demands and various government discrimination test calculations, and providing employees and retirees with understandable 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 satisfy 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 Social Security (United States)|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.

Actuarial science applied to other forms of insurance

Actuarial science is also applied to Property insurance|Property, Casualty insurance|Casualty, Liability insurance, and General insurance. In these forms of insurance, coverage is generally provided on a renewable period, (such as a yearly). Coverage can be cancelled at the end of the period by either party.

Property insurance|property and casualty insurance companies tend to specialize because of the complexity and diversity of risks. One division is to organize around personal and commercial lines of insurance. Personal lines of insurance are for individuals and include fire, auto, homeowners, theft and umbrella coverages. Commercial lines address the insurance needs of businesses and include property, business continuation, product liability, fleet/commercial vehicle, workers compensation, fidelity & surety, and Directors and officers liability insurance|D&O insurance. The insurance industry also provides coverage for exposures such as catastrophe, weather-related risks, earthquakes, patent infringement and other forms of corporate espionage, terrorism, and "one-of-a-kind" (e..g, satellite launch). Actuarial science provides data collection, measurement, estimating, forecasting, and valuation tools to provide financial and underwriting data for management to assess marketing opportunities and the nature of the risks. Actuarial science often helps to assess the overall risk from catastrophic events in relation to its underwriting capacity or surplus.

  • In the reinsurance fields, actuarial science can be used to design and price reinsurance and retro-reinsurance schemes, and to establish reserve funds for known claims and future claims and catastrophes.


In the ancient world there was no room for the sick, suffering, disabled, aged, or the poor???it was not part of the Collective consciousness|cultural consciousness of societies . Early methods of protection involved Charitable organization|charity; Religion-supporting organization|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 Ancient Rome|Rome . Charitable protection is still an active form of support to this very day . However, receiving charity is uncertain and is often accompanied by social stigma. Elementary mutual aid (organization)|mutual aid agreements and pensions did arise in antiquity . Early in the Roman Empire|Roman empire, associations were formed to meet the expenses of burial, cremation, and monuments???precursors to Burial society|burial insurance and Friendly society|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 Columbarium|columb??ria, or burial vaults, owned by the fund???the precursor to Mutual insurance|mutual insurance companies . 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 . However, many of these earlier forms of surety and aid would often fail due to lack of understanding and knowledge .

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 (statistics)|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 to 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 (of Halley's comet fame). In addition to constructing his own life table, Halley demonstrated a method of using his life table to calculate the Insurance|premium or amount of money someone of a given age should pay to purchase a life-annuity .

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 The Equitable Life Assurance Society|Equitable Life) in London in 1762. The company still exists, though it has encountered 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 . Other companies that did not originally use such mathematical and scientific methods most often failed or were forced to adopt the methods pioneered by Equitable .

Effects of technology
In the 18th and 19th 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 . 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 . 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 . In the 1930s and 1940s, however, the rigorous mathematical foundations for stochastic processes were developed . 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 .

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 sheer complexity of calculations, and the second with the heavy burden of regulations resulting from the Armstrong investigation of 1905, the Glass-Steagall 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 . As a result, actuarial science developed along a different path, becoming more reliant on assumptions, as opposed to the arbitrage-free Rational pricing#Risk neutral valuation|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 . 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. . Ideas from financial economics became increasingly influential in actuarial thinking, and actuarial science has started to embrace more sophisticated mathematical modelling of finance . 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 . 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 principles:
# financial models should be free of arbitrage
# assets and liabilities with identical cash flows should have the same price. This, of course, is at odds with FASB
# the value of an asset is independent of its financing
# 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. .

Actuaries outside insurance
There is an increasing trend to recognize that actuarial skills can be applied to a range of applications outside the insurance industry. One notable example is the use in some US states of actuarial models to set criminal sentencing guidelines. These models attempt to predict the chance of re-offending according to rating factors which include the type of crime, age, educational background and ethnicity of the offender . However, these models have been open to criticism as providing justification by law enforcement personnel on specific ethnic groups. Whether or not this is statistically correct or a self-fulfilling correlation remains under debate .

Another example is the use of actuarial models to assess the risk of sex offense recidivism. Actuarial models and associated tables, such as the MnSOST-R, Static-99, and SORAG, have been used since the late 1990s to determine the likelihood that a sex offender will recidivate and thus whether he or she should be institutionalized or set free .


See also

  • Actuarial control cycle

  • Actuarial exam

  • :Category:Actuarial associations

  • Data mining

  • List of actuarial topics

  • Ruin theory


Works cited


External links

  • http://fastfound.com/study-in-australia/science/actuarial-science-statistics-degrees/ Actuarial Science studies at Australian Universities

Category:Actuarial science|*
Category:Formal sciences
Category:Fields of application of statistics

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This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "actuarial science".

Last Modified:   2010-12-03

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