Actuarial science

Last updated

2003 US mortality (life) table, Table 1, Page 1 Excerpt from CDC 2003 Table 1.pdf
2003 US mortality (life) table, Table 1, Page 1

Actuarial science is the discipline that applies mathematical and statistical methods to assess risk in insurance, pension, finance, investment and other industries and professions. More generally, actuaries apply rigorous mathematics to model matters of uncertainty and life expectancy.

Contents

Actuaries are professionals trained in this discipline. In many countries, actuaries must demonstrate their competence by passing a series of rigorous professional examinations focused in fields such as probability and predictive analysis.

Actuarial science includes a number of interrelated subjects, including mathematics, probability theory, statistics, finance, economics, financial accounting and computer science. Historically, actuarial science used deterministic models in the construction of tables and premiums. The science has gone through revolutionary changes since the 1980s due to the proliferation of high speed computers and the union of stochastic actuarial models with modern financial theory. [1]

Many universities have undergraduate and graduate degree programs in actuarial science. In 2010,[ needs update ] a study published by job search website CareerCast ranked actuary as the #1 job in the United States. [2] The study used five key criteria to rank jobs: environment, income, employment outlook, physical demands, and stress. In 2023, U.S. News & World Report ranked actuary as the eighth best job in the business sector and the thirteenth best job in STEM. [3]

Subfields

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 coverage 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. Certain aspects of the actuarial methods for discounting pension funds have come under criticism from modern financial economics.[ citation needed ]

Applications to other forms of insurance

Actuarial science is also applied to property, casualty, liability, 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.[ citation needed ]

Property and casualty insurance companies tend to specialize because of the complexity and diversity of risks.[ citation needed ] 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 and surety, and 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.[ citation needed ]

In the reinsurance fields, actuarial science can be used to design and price reinsurance and retrocession arrangements, and to establish reserve funds for known claims and future claims and catastrophes.[ citation needed ]

Actuaries in criminal justice

There is an increasing trend to recognize that actuarial skills can be applied to a range of applications outside the traditional fields of insurance, pensions, etc. 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. [7] However, these models have been open to criticism as providing justification for discrimination against specific ethnic groups by law enforcement personnel. Whether this is statistically correct or a self-fulfilling correlation remains under debate. [8]

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 re-offend and thus whether he or she should be institutionalized or set free. [9]

Traditional actuarial science and modern financial economics in the US have different practices, which is caused by different ways of calculating funding and investment strategies, and by different regulations.[ citation needed ]

Regulations are 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, which cushioned market fluctuations, and the Financial Accounting Standards Board, (FASB) in the US and Canada, which regulates pensions valuations and funding.[ citation needed ]

History

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. [10]

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.[ citation needed ]

The potential of modern financial economics theory to complement existing actuarial science was recognized by actuaries in the mid-twentieth century. [11] 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. [12] Ideas from financial economics became increasingly influential in actuarial thinking, and actuarial science has started to embrace more sophisticated mathematical modelling of finance. [13] 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. [14] However, assumption-dependent concepts are still widely used (such as the setting of the discount rate assumption as mentioned earlier), particularly in North America.[ citation needed ]

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:

  1. financial models should be free of arbitrage.
  2. assets and liabilities with identical cash flows should have the same price. This is at odds with FASB.
  3. the value of an asset is independent of its financing.
  4. 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. [15]

Pre-formalisation

Elementary mutual aid agreements and pensions arose in antiquity. [16] Early in the Roman empire, associations were formed to meet the expenses of burial, cremation, and monuments—precursors 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. [17] 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 forebears, and to Celtic society. [18] However, many of these earlier forms of surety and aid would often fail due to lack of understanding and knowledge. [19]

Initial development

The 17th century was a period of 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 of 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, the father of demography, John Graunt, who showed that there were predictable patterns of longevity and death in a group, or cohort, of people of the same age, despite the uncertainty of the date of death of any one individual. This study became the basis for the original life table. One could now 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). Halley constructed his own life table, and showed how it could be used to calculate the premium amount someone of a given age should pay to purchase a life annuity. [20]

Early actuaries

James Dodson's pioneering work on the long term insurance contracts under which the same premium is charged each year led to the formation of the Society for Equitable Assurances on Lives and Survivorship (now commonly known as Equitable Life) in London in 1762. [21] William Morgan is often considered the father of modern actuarial science for his work in the field in the 1780s and 90s. Many other life insurance companies and pension funds were created over the following 200 years. Equitable Life was the first to use the word "actuary" for its chief executive officer in 1762. [22] Previously, "actuary" meant an official who recorded the decisions, or "acts", of ecclesiastical courts. [19] Other companies that did not use such mathematical and scientific methods most often failed or were forced to adopt the methods pioneered by Equitable. [23]

Technological advances

In the 18th and 19th centuries, calculations were performed without computers. The computations of life insurance premiums and reserving requirements are rather complex, and actuaries developed techniques to make the calculations as easy as possible, for example "commutation functions" (essentially precalculated columns of summations over time of discounted values of survival and death probabilities). [24] Actuarial organizations were founded to support and further both actuaries and actuarial science, and to protect the public interest by promoting competency and ethical standards. [25] However, calculations remained cumbersome, and actuarial shortcuts were commonplace. Non-life actuaries followed in the footsteps of their life insurance colleagues during the 20th century. The 1920 revision for the New-York based National Council on Workmen's Compensation Insurance rates took over two months of around-the-clock work by day and night teams of actuaries. [26] In the 1930s and 1940s, the mathematical foundations for stochastic processes were developed. [27] Actuaries could now begin to estimate losses using models of random events, instead of the deterministic methods they had used in the past. The introduction and development of the computer 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 rapidly improved, while still being heavily dependent on the assumptions input into the models, and actuaries needed to adjust to this new world . [28]

See also

Related Research Articles

<span class="mw-page-title-main">Actuary</span> Analyst of business risk and uncertainty

An actuary is a professional with advanced mathematical skills who deals with the measurement and management of risk and uncertainty. The name of the corresponding field is actuarial science which covers rigorous mathematical calculations in areas of life expectancy and life insurance. These risks can affect both sides of the balance sheet and require asset management, liability management, and valuation skills. Actuaries provide assessments of financial security systems, with a focus on their complexity, their mathematics, and their mechanisms.

<span class="mw-page-title-main">International Actuarial Association</span>

The International Actuarial Association (IAA) is a worldwide association of local professional actuarial associations.

<span class="mw-page-title-main">Society of Actuaries</span> Actuary Organization

The Society of Actuaries (SOA) is a global professional organization for actuaries. It was founded in 1949 as the merger of two major actuarial organizations in the United States: the Actuarial Society of America and the American Institute of Actuaries. It is a full member organization of the International Actuarial Association.

<span class="mw-page-title-main">Casualty Actuarial Society</span>

The Casualty Actuarial Society (CAS) is a professional society of actuaries in North America specializing in property and casualty insurance.

<span class="mw-page-title-main">Life insurance</span> Type of contract

Life insurance is a contract between an insurance policy holder and an insurer or assurer, where the insurer promises to pay a designated beneficiary a sum of money upon the death of an insured person. Depending on the contract, other events such as terminal illness or critical illness can also trigger payment. The policyholder typically pays a premium, either regularly or as one lump sum. The benefits may include other expenses, such as funeral expenses.

The Institute of Actuaries was one of the two professional bodies which represented actuaries in the United Kingdom. The institute was based in England, while the other body, the Faculty of Actuaries, was based in Scotland. While the Institute and Faculty of Actuaries were separate institutions, they worked very closely together, and their professional qualifications and actuarial standards were identical. On 25 May 2010, voting members of the institute who took part in a ballot voted to merge the institute with the faculty, thus creating the Institute and Faculty of Actuaries, which came into being on 1 August 2010. The Institute of Actuaries ceased to exist on that date.

The Faculty of Actuaries in Scotland was the professional body representing actuaries in Scotland. The Faculty of Actuaries was one of two actuarial bodies in the UK, the other was the Institute of Actuaries, which was a separate body in England, Wales and Northern Ireland. While the Faculty of Actuaries and the Institute of Actuaries were separate institutions, they worked very closely together, and the professional qualifications and professional standards for actuaries were identical in each of them. On 25 May 2010, voting members of the Faculty who took part in a ballot voted to merge the Faculty with the Institute of Actuaries, thus creating the Institute and Faculty of Actuaries which came into being on 1 August 2010, superseding the Faculty of Actuaries which ceased to exist on that date.

The following outline is provided as an overview of and topical guide to actuarial science:

Under European Union law, an annuity is a financial contract which provides an income stream in return for an initial payment with specific parameters. It is the opposite of a settlement funding. A Swiss annuity is not considered a European annuity for tax reasons.

Credibility theory is a branch of actuarial mathematics concerned with determining risk premiums. To achieve this, it uses mathematical models in an effort to forecast the (expected) number of insurance claims based on past observations. Technically speaking, the problem is to find the best linear approximation to the mean of the Bayesian predictive density, which is why credibility theory has many results in common with linear filtering as well as Bayesian statistics more broadly.

The following outline is provided as an overview of and topical guide to finance:

A life annuity is an annuity, or series of payments at fixed intervals, paid while the purchaser is alive. The majority of life annuities are insurance products sold or issued by life insurance companies however substantial case law indicates that annuity products are not necessarily insurance products.

<span class="mw-page-title-main">Anders Lindstedt</span> Swedish mathematician and astronomer (1854–1939)

Anders Lindstedt was a Swedish mathematician, astronomer, and actuarial scientist, known for the Lindstedt-Poincaré method.

Milliman, formerly Milliman & Robertson, is an international actuarial and consulting firm based in Seattle, Washington.

<span class="mw-page-title-main">Institute and Faculty of Actuaries</span> UK professional body

The Institute and Faculty of Actuaries is the professional body which represents and regulates actuaries in the United Kingdom.

<span class="mw-page-title-main">Philip Booth (economist)</span> British economist

Philip Booth is a British economist. He is Dean of the Faculty of Education, Humanities and Social Sciences at St Mary's University, Twickenham, and Senior Academic Fellow at the Institute of Economic Affairs. His primary areas of research and writing are social insurance, financial regulation and Catholic social teaching.

The actuarial credentialing and exam process usually requires passing a rigorous series of professional examinations, most often taking several years in total, before one can become recognized as a credentialed actuary. In some countries, such as Denmark, most study takes place in a university setting. In others, such as the U.S., most study takes place during employment through a series of examinations. In the UK, and countries based on its process, there is a hybrid university-exam structure.

<span class="mw-page-title-main">James Waterman Glover</span> American mathematician, statistician and actuary

James Waterman Glover was an American mathematician, statistician, and actuary.

Patrick L. Brockett is an endowed Chaired Professor within the Information, Risk and Operations Management, Finance, and Mathematics departments at The University of Texas at Austin. He is the Director of the Risk Management and Insurance Program, Director for the Center of Risk Management and Insurance, and Director for the Minor/Certificate in Risk Management Program. He is also an Affiliated Faculty Member in the University of Texas- Austin Division of Statistics & Scientific Computation. He is known for his research in statistics, probability, actuarial science, quantitative methods in business and social sciences, and risk and insurance. The American Risk and Insurance Association (ARIA) endowed and named a research award in his honor: The Patrick Brockett & Arnold Shapiro Actuarial Research Award, awarded to the actuarial journal article that makes the best contribution of interest to ARIA risk management and insurance researchers.

References

  1. Frees 1990.
  2. Needleman 2010.
  3. U.S. News & World Report 2023.
  4. Hsiao 2001.
  5. Hsiao 2004.
  6. CHBRP 2004.
  7. Silver & Chow-Martin 2002.
  8. Harcourt 2003.
  9. Nieto & Jung 2006, pp. 28–33.
  10. Whelan 2002.
  11. Bühlmann 1997, pp. 169–171.
  12. D'Arcy 1989.
  13. Economist 2006.
  14. Feldblum 2001, pp. 8–9.
  15. Moriarty 2006.
  16. Thucydides.
  17. Johnston 1932, §475–§476.
  18. Loan 1992.
  19. 1 2 Faculty and Institute of Actuaries 2004.
  20. Halley 1693.
  21. Lewin 2007, p. 38.
  22. Ogborn 1956, p. 235.
  23. Bühlmann 1997, p. 166.
  24. Slud 2006.
  25. Hickman 2004, p. 4.
  26. Michelbacher 1920, pp. 224, 230.
  27. Bühlmann 1997, p. 168.
  28. MacGinnitie 1980, pp. 50–51.

Works cited

Bibliography