2003 US mortality (life) table, Table 1, Page 1

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. Image File history File links Download high resolution version (900x1189, 108 KB) Summary Licensing File links The following pages on the English Wikipedia link to this file (pages on other projects are not listed): Actuary Actuarial science Life table ... Image File history File links Download high resolution version (900x1189, 108 KB) Summary Licensing File links The following pages on the English Wikipedia link to this file (pages on other projects are not listed): Actuary Actuarial science Life table ... 2003 US mortality table, Table 1, Page 1 In actuarial science, a life table (also called a mortality table or actuarial table) is a table which shows, for a person at each age, what the probability is that they die before their next birthday. ... Euclid, Greek mathematician, 3rd century BC, known today as the father of geometry; shown here in a detail of The School of Athens by Raphael. ... A graph of a bell curve in a normal distribution showing statistics used in educational assessment, comparing various grading methods. ... Finance studies and addresses the ways in which individuals, businesses, and organizations raise, allocate, and use monetary resources over time, taking into account the risks entailed in their projects. ... The examples and perspective in this article or section may not represent a worldwide view. ... Risk is a concept which relates to human expectations. ... Damage from Hurricane Katrina. ...

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). This article does not cite its references or sources. ... A graph of a bell curve in a normal distribution showing statistics used in educational assessment, comparing various grading methods. ... Finance studies and addresses the ways in which individuals, businesses, and organizations raise, allocate, and use monetary resources over time, taking into account the risks entailed in their projects. ... Face-to-face trading interactions among on the New York Stock Exchange trading floor Economics, as a social science, studies the production, distribution, and consumption of commodities. ... Stochastic, from the Greek stochos or goal, means of, relating to, or characterized by conjecture; conjectural; random. ...

Many universities have undergraduate and graduate degree programs in actuarial science. In 2002, a Wall Street Journal survey on the best jobs in the United States listed “actuary” as the second best job, while in previous editions of the list, actuaries had been the top rated job (Lee 2002). The Wall Street Journal is an influential international daily newspaper published in New York City, New York with an average daily circulation of 1,800,607 (2002). ...

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. It has been suggested that Life assurance be merged into this article or section. ... The present value of a future cash flow is the nominal amount of money to change hands at some future date, discounted to account for the time value of money. ... Collective agreement is a labor contract between an employer and one or more unions. ... Financial economics is the branch of economics concerned with resource allocation over time. ...

• 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. Contemporary life insurance programs have been extended to include credit and mortgage insurance, key man insurance for small businesses, long term care insurance and health savings accounts (Hsiao 2001).

• In health insurance, including insurance provided directly by employers, and social insurance, actuarial science focuses on the analyses 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. (Hsiao 1988) Actuarial science also aids in the design of benefit structures, reimbursement standards, and the effects of proposed government 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 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 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.

2003 US mortality table, Table 1, Page 1 In actuarial science, a life table (also called a mortality table or actuarial table) is a table which shows, for a person at each age, what the probability is that they die before their next birthday. ... Interest is the rent paid to borrow money. ... The examples and perspective in this article or section may not represent a worldwide view. ... It has been suggested that this section be split into a new article entitled Medical Savings Account. ... Resource-Based Relative Value Scale (RBRVS) is a scheme used to determine how much money doctors should be paid. ... Collective agreement is a labor contract between an employer and one or more unions. ... The Financial Accounting Standards Board (FASB) is a private, non-for-profit organization whose primary purpose is to develop Generally Accepted Accounting Principles in the United States (US GAAP). ... The Office of the Chief Actuary is an organizational entity within both of the governments of the United States and Canada. ... The United States Social Security Administration (or SSA[1]) is an independent agency of the United States government established by a law currently codified at . ... Social Security, in the United States, refers to the Federal Old-Age, Survivors, and Disability Insurance (OASDI) program. ... Supplemental Security Income is a monthly stipend provided to some citizens by the United States federal government. ...

Actuarial science applied to other forms of insurance

Actuarial science is also applied to short term forms of insurance, referred to as Property & Casualty or Liability insurance, or General insurance. In these forms of insurance, coverage is generally provided on a renewable annual period, (such as a yearly contract to provide homeowners insurance policy covering damage to a house and its contents for one year). Coverage can be cancelled at the end of the period by either party. Property insurance provides protection against risks to property, such as fire, theft or weather damage. ... Casualty insurance is a broad category of insurance that includes almost any coverage that is not related to life, health, or property. ... In the most general sense, a liability is anything that is a hindrance, or puts one at a disadvantage. ... A General is an officer of high military rank. ...

• In the property & casualty insurance fields, companies tend to specialize because of the complexity and diversity of risks. A convenient division is to organize around personal and commercial lines of insurance. Personal lines of insurance include the familiar fire, auto, homeowners, theft and umbrella coverages. Commercial lines would include business continuation, product liability, fleet insurance, workers compensation, fidelity & surety, D&O insurance and a great variety of coverages required for businesses. Beyond these, the industry needs to provide catastrophe insurance for weather related risks, earthquakes, patent infringement and other forms of corporate espionage, terrorism and all its implications, and finally coverage for the most unusual risks sometimes associated with Lloyds of London. In all of these ventures, actuarial science has to bring data collection, measurement, estimating, forecasting, and valuation tools to provide financial and underwriting data for management to assess marketing opportunities and the degree of risk taking that is required. Actuarial science needs to operate at two levels: (i) at the product level to facilitate politically correct equitable pricing and reserving; and (ii) at the corporate level to assess the overall risk to the enterprise from catastrophic events in relation to its underwriting capacity or surplus. Actuaries, usually working in a multidisciplinary team must help answer management issues: (i) is the risk insurable; (ii) does the company have effective claims administration to determine damages; (iii) does the company have sufficient claims handling to cover catastrophic events; (iv) and the vulnerability of the enterprise to uncontrollable risks such as inflation, adverse political outcomes; unfavorable legal outcomes such as excess punitive damage awards, and international turmoil.

• In the reinsurance fields, actuarial science is used to design and price reinsurance and retro-reinsurance schemes, and to establish reserve funds for known claims and future claims and catastrophes. Retro-reinsurance, also known as retrocession occurs when a reinsurance company reinsures risks with yet another reinsurance company. Reinsurance can be used to spread the risk, to smooth earnings and cash flow, to reduce reserve requirements and improve the quality of surplus, Reinsurance creates arbitrage situations, and retro-reinsurance arbitrage can create Spirals which can lead to financial instability and bankruptcies. A spiral occurs (as an example) when a reinsurer accepts a retrocession which unknowingly contains risks that were previously reinsured. Some reported cases of arbitrage and spirals have been found to be illegal. The Equity Funding scam was built on the abusive use of financial reinsurance to transfer capital funds from the reinsurance carrier to Equity Funding. In the broadest sense of the word, reinsurance takes many forms: (i) declining a risk; (ii) requiring the insured to self insure part of the contingent or investment risk; (iii) limiting the coverage through deductibles, coinsurance or exclusionary policy language; (iv) placing a policy in a risk pool with a cohort of competitors to achieve a social objective; (v) ceding or transferring a percentage of each policy to another insurance company (i.e. the reinsurer); (vi) ceding or transferring excess amounts or excess coverages to the reinsurer; (vii) ceding or transferring asset based policies to the reinsurer in exchange for capital; (viii) purchasing stop loss insurance; (ix) purchasing umbrella coverages for a basket of risks; (x) purchasing catastrophe insurance for specific contingent events. Reinsurance is complex. Company management and their actuaries need to deal with all the known insurable contingent events, as well as underwrite the quality of their cedant companies, and maintain the information tools and auditing practices to identify arbitrage and spirals.

Property insurance provides protection against risks to property, such as fire, theft or weather damage. ... Casualty insurance is a broad category of insurance that includes almost any coverage that is not related to life, health, or property. ... Directors and officers liability insurance - Wikipedia, the free encyclopedia /**/ @import /skins-1. ... Lloyds of London is a British insurance market. ... Reinsurance is a means by which an insurance company can protect itself against the risk of losses with other insurance companies. ... In economics, arbitrage is the practice of taking advantage of a state of imbalance between two or more markets: a combination of matching deals are struck that capitalize upon the imbalance, the profit being the difference between the market prices. ... In economics, arbitrage is the practice of taking advantage of a state of imbalance between two or more markets: a combination of matching deals are struck that capitalize upon the imbalance, the profit being the difference between the market prices. ... Equity Funding Corporation of America was a Los Angeles-based U.S. financial conglomerate that marketed a package of mutual funds and life insurance to private individuals in the 1960s and 70s. ... Financial reinsurance, also known as fin re, is a form of reinsurance which is focused more on capital management than on risk transfer. ...

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—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 (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). To meet Wikipedias quality standards, this article or section may require cleanup. ... A charitable organization (also known as a charity) is a trust, company or unincorporated association established for charitable purposes only. ... Religious activities generally need some infrastructure to be conducted. ... (2nd century - 3rd century - 4th century - other centuries) Events The Sassanid dynasty of Persia launches a war to reconquer lost lands in the Roman east. ... This article or section may contain original research or unverified claims. ... Social stigma refers to severe social disapproval of personal characteristics that is against cultural norms. ... The term mutual aid has multiple meanings. ... The Roman Empire is the name given to both the imperial domain developed by the city-state of Rome and also the corresponding phase of that civilization, characterized by an autocratic form of government. ... Burial societies are a form of friendly society. ... A friendly society (sometimes called a mutual society, benevolent society or fraternal organization) is a mutual association for insurance-like purposes, and often, especially in the past, serving ceremonial and friendship purposes also. ... Columbarium niches built into the side of St. ... Mutual insurance is a type of insurance where those protected by the insurance (policyholders) also own the organization. ... A surety is a person who agrees to be responsible for the debt or obligation of another. ... Assurance has been defined by the American Institute of Certified Public Accountants (AICPA) as Independent Professional Services that improve information quality or its context. Such services are very broad and could include assessments of internet security and quality of health facilities. ...

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). (16th century - 17th century - 18th century - more centuries) As a means of recording the passage of time, the 17th century was that century which lasted from 1601-1700. ... Compound interest, is interest which is added to the original principal. ... Probability theory is the mathematical study of phenomena characterized by randomness or uncertainty. ... The term draper can refer to a number of individuals and places. ... John Graunt (1620-1674) was one of the first demographers. ... For other meanings see cohort In statistics and demography, a cohort is a group of subjects — most often humans from a given population — defined by a condition on their date of birth. ... 2003 US mortality table, Table 1, Page 1 In actuarial science, a life table (also called a mortality table or actuarial table) is a table which shows, for a person at each age, what the probability is that they die before their next birthday. ... Portrait of Edmond Halley painted around 1687 by Thomas Murray (Royal Society, London) Portrait of Edmond Halley Bust of Edmond Halley in the Museum of the Royal Greenwich Observatory Edmond Halley (sometimes Edmund, November 8, 1656 – January 14, 1742) was an English astronomer, geophysicist, mathematician, meteorologist, and physicist. ... The examples and perspective in this article or section may not represent a worldwide view. ...

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). Equitable Life (founded 1762) is a pension company in the United Kingdom. ...

Effects of technology

In the 18th century 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). (17th century - 18th century - 19th century - more centuries) As a means of recording the passage of time, the 18th century refers to the century that lasted from 1701 through 1800. ... Alternative meaning: Nineteenth Century (periodical) (18th century — 19th century — 20th century — more centuries) As a means of recording the passage of time, the 19th century was that century which lasted from 1801-1900 in the sense of the Gregorian calendar. ... (19th century - 20th century - 21st century - more centuries) Decades: 1900s 1910s 1920s 1930s 1940s 1950s 1960s 1970s 1980s 1990s As a means of recording the passage of time, the 20th century was that century which lasted from 1901–2000 in the sense of the Gregorian calendar (1900–1999... Stochastic, from the Greek stochos or goal, means of, relating to, or characterized by conjecture; conjectural; random. ... The term deterministic may refer to: the more general notion of determinism from philosophy, see determinism a type of algorithm as discussed in computer science, see deterministic algorithm scientific determinism as used by Karl Popper and Stephen Hawking deterministic system in mathematics deterministic system in philosophy deterministic finite state machine...

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-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. Financial economics is the branch of economics concerned with resource allocation over time. ... The Glass-Steagal Act of 1933 separated commercial and merchant investment banking. ... The National Association of Insurance Commissioners (NAIC) is an IRS 501(c)(3) non-profit organization which seeks to organize the regulatory and supervisory efforts of the state Insurance Commissioners around the United States. ... The Financial Accounting Standards Board (FASB) is a private, non-for-profit organization whose primary purpose is to develop Generally Accepted Accounting Principles in the United States (US GAAP). ...

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. In economics, arbitrage is the practice of taking advantage of a state of imbalance between two (or possibly more) markets: a combination of matching deals are struck that exploit the imbalance, the profit being the difference between the market prices. ... Rational pricing is the assumption in financial economics that asset prices (and hence asset pricing models) will reflect the arbitrage-free price of the asset as any deviation from this price will be arbitraged away. This assumption is useful in pricing fixed income securities, particularly bonds, and is fundamental to... Asset allocation is a concept of determining and maintaining a plan of investment in terms of a chosen mix of investments in different assets. ... The term discount rate is used in several different contexts: // Credit cards Main article: Merchant account The discount rate is a percentage of the dollar amount of the transaction that a merchant is charged for each credit card transaction. ... Financial economics is the branch of economics concerned with resource allocation over time. ...

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). The Financial Accounting Standards Board is a major organization to develop Generally Accepted Accounting Principles in the United States (US GAAP) along with SEC, AICPA, and GASB. It was created in 1973 and replaced its predecessor, the Accounting Principles Board and the Committee on Accounting Procedure of the American Institute...

Actuaries outside insurance

There is an increasing trend to recognise 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 (Silver and Chow-Martin 2002).

These studies have been criticised for justifying a focus by police on "trouble" ethnic groups and for ignoring the fact that not all suspects have an equal chance of being charged and convicted, which skews the data.^{[citation needed]}

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 (Nieto and Jung 2006 pp. 28–33).

See also

• Category:Actuarial associations
• Category:Actuarial science

References

Works Cited

Bibliography

• Charles L. Trowbridge (1989). "Fundamental Concepts of Actuarial Science" (PDF). Revised Edition. Actuarial Education and Research Fund. Retrieved on 2006-06-28.