Actuarial science
Overview

Actuarial science is the discipline that applies mathematical
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

and statistical
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....

methods to assess risk
Risk assessment
Risk assessment is a step in a risk management procedure. Risk assessment is the determination of quantitative or qualitative value of risk related to a concrete situation and a recognized threat...

in the insurance
Insurance
In law and economics, insurance is a form of risk management primarily used to hedge against the risk of a contingent, uncertain loss. Insurance is defined as the equitable transfer of the risk of a loss, from one entity to another, in exchange for payment. An insurer is a company selling the...

and finance
Finance
"Finance" is often defined simply as the management of money or “funds” management Modern finance, however, is a family of business activity that includes the origination, marketing, and management of cash and money surrogates through a variety of capital accounts, instruments, and markets created...

industries. Actuaries
Actuary
An actuary is a business professional who deals with the financial impact of risk and uncertainty. Actuaries provide expert assessments of financial security systems, with a focus on their complexity, their mathematics, and their mechanisms ....

are professionals who are qualified in this field through education and experience. In many countries, actuaries must demonstrate their competence by passing a series of rigorous professional examinations.

Actuarial science includes a number of interrelating subjects, including probability
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...

, mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, statistics
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....

, finance
Finance
"Finance" is often defined simply as the management of money or “funds” management Modern finance, however, is a family of business activity that includes the origination, marketing, and management of cash and money surrogates through a variety of capital accounts, instruments, and markets created...

, economics
Economics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...

, financial economics
Financial economics
Financial Economics is the branch of economics concerned with "the allocation and deployment of economic resources, both spatially and across time, in an uncertain environment"....

, and computer programming
Computer programming
Computer programming is the process of designing, writing, testing, debugging, and maintaining the source code of computer programs. This source code is written in one or more programming languages. The purpose of programming is to create a program that performs specific operations or exhibits a...

.
Encyclopedia
Actuarial science is the discipline that applies mathematical
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

and statistical
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....

methods to assess risk
Risk assessment
Risk assessment is a step in a risk management procedure. Risk assessment is the determination of quantitative or qualitative value of risk related to a concrete situation and a recognized threat...

in the insurance
Insurance
In law and economics, insurance is a form of risk management primarily used to hedge against the risk of a contingent, uncertain loss. Insurance is defined as the equitable transfer of the risk of a loss, from one entity to another, in exchange for payment. An insurer is a company selling the...

and finance
Finance
"Finance" is often defined simply as the management of money or “funds” management Modern finance, however, is a family of business activity that includes the origination, marketing, and management of cash and money surrogates through a variety of capital accounts, instruments, and markets created...

industries. Actuaries
Actuary
An actuary is a business professional who deals with the financial impact of risk and uncertainty. Actuaries provide expert assessments of financial security systems, with a focus on their complexity, their mathematics, and their mechanisms ....

are professionals who are qualified in this field through education and experience. In many countries, actuaries must demonstrate their competence by passing a series of rigorous professional examinations.

Actuarial science includes a number of interrelating subjects, including probability
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...

, mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, statistics
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....

, finance
Finance
"Finance" is often defined simply as the management of money or “funds” management Modern finance, however, is a family of business activity that includes the origination, marketing, and management of cash and money surrogates through a variety of capital accounts, instruments, and markets created...

, economics
Economics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...

, financial economics
Financial economics
Financial Economics is the branch of economics concerned with "the allocation and deployment of economic resources, both spatially and across time, in an uncertain environment"....

, and computer programming
Computer programming
Computer programming is the process of designing, writing, testing, debugging, and maintaining the source code of computer programs. This source code is written in one or more programming languages. The purpose of programming is to create a program that performs specific operations or exhibits a...

. 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
Stochastic
Stochastic refers to systems whose behaviour is intrinsically non-deterministic. A stochastic process is one whose behavior is non-deterministic, in that a system's subsequent state is determined both by the process's predictable actions and by a random element. However, according to M. Kac and E...

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
Life insurance
Life insurance is a contract between an insurance policy holder and an insurer, where the insurer promises to pay a designated beneficiary a sum of money upon the death of the insured person. Depending on the contract, other events such as terminal illness or critical illness may also trigger...

, 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
Present value
Present value, also known as present discounted value, is the value on a given date of a future payment or series of future payments, discounted to reflect the time value of money and other factors such as investment risk...

of a future sum. Pensions and healthcare emerged in the early 20th century as a result of collective bargaining
Collective bargaining
Collective bargaining is a process of negotiations between employers and the representatives of a unit of employees aimed at reaching agreements that regulate working conditions...

. Certain aspects of the actuarial methods for discounting pension funds have come under criticism from modern financial economics
Financial economics
Financial Economics is the branch of economics concerned with "the allocation and deployment of economic resources, both spatially and across time, in an uncertain environment"....

.
• In traditional life insurance, actuarial science focuses on the analysis of mortality
Mortality rate
Mortality rate is a measure of the number of deaths in a population, scaled to the size of that population, per unit time...

, the production of life table
Life table
In actuarial science, a life table is a table which shows, for each age, what the probability is that a person of that age will die before his or her next birthday...

s, and the application of compound interest
Interest
Interest is a fee paid by a borrower of assets to the owner as a form of compensation for the use of the assets. It is most commonly the price paid for the use of borrowed money, or money earned by deposited funds....

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
Long term care insurance
Long-term care insurance , an insurance product sold in the United States, United Kingdom and Canada, helps provide for the cost of long-term care beyond a predetermined period...

and health savings accounts
Medical savings account
Medical savings account refers to an account in which tax-deferred deposits can be made for medical expenses.-In Singapore:Medisave was introduced in April 1984 as a national medical savings system for Singaporeans...

.

• 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
Collective bargaining
Collective bargaining is a process of negotiations between employers and the representatives of a unit of employees aimed at reaching agreements that regulate working conditions...

; 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
Financial Accounting Standards Board
The Financial Accounting Standards Board is a private, not-for-profit organization whose primary purpose is to develop generally accepted accounting principles within the United States in the public's interest...

(FASB).

• In social welfare programs, the Office of the Chief Actuary
Office of the Chief Actuary
The Office of the Chief Actuary is an organizational entity within both of the governments of the United States and Canada. The Office has responsibility for actuarial estimates regarding social welfare programs like Social Security and the Canadian Old Age Security System...

The United States Social Security Administration is an independent agency of the United States federal government that administers Social Security, a social insurance program consisting of retirement, disability, and survivors' benefits...

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
Social Security (United States)
In the United States, Social Security refers to the federal Old-Age, Survivors, and Disability Insurance program.The original Social Security Act and the current version of the Act, as amended encompass several social welfare and social insurance programs...

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
Supplemental Security Income
Supplemental Security Income is a United States government program that provides stipends to low-income people who are either aged , blind, or disabled. Although administered by the Social Security Administration, SSI is funded from the U.S. Treasury general funds, not the Social Security trust fund...

(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
Property insurance
Property insurance provides protection against most risks to property, such as fire, theft and some weather damage. This includes specialized forms of insurance such as fire insurance, flood insurance, earthquake insurance, home insurance or boiler insurance. Property is insured in two main...

, Casualty
Casualty insurance
Casualty insurance, often equated to liability insurance, is used to describe an area of insurance not directly concerned with life insurance, health insurance, or property insurance. It is mainly used to describe the liability coverage of an individual or organization's for negligent acts or...

, Liability insurance
Liability insurance
Liability insurance is a part of the general insurance system of risk financing to protect the purchaser from the risks of liabilities imposed by lawsuits and similar claims. It protects the insured in the event he or she is sued for claims that come within the coverage of the insurance policy...

, and General insurance
General insurance
General insurance or non-life insurance policies, including automobile and homeowners policies, provide payments depending on the loss from a particular financial event. General insurance typically comprises any insurance that is not determined to be life insurance. It is called property and...

. 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
Property insurance
Property insurance provides protection against most risks to property, such as fire, theft and some weather damage. This includes specialized forms of insurance such as fire insurance, flood insurance, earthquake insurance, home insurance or boiler insurance. Property is insured in two main...

and casualty insurance
Casualty insurance
Casualty insurance, often equated to liability insurance, is used to describe an area of insurance not directly concerned with life insurance, health insurance, or property insurance. It is mainly used to describe the liability coverage of an individual or organization's for negligent acts or...

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 D&O
Directors and officers liability insurance
Directors and Officers Liability Insurance is liability insurance payable to the directors and officers of a company, or to the organization itself, to cover damages or defense costs in the event they suffer such losses as a result of a lawsuit for alleged wrongful acts while acting in their...

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
Reinsurance
Reinsurance is insurance that is purchased by an insurance company from another insurance company as a means of risk management...

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.

### 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
Collective consciousness
Collective consciousness was a term coined by the French sociologist Émile Durkheim to refer to the shared beliefs and moral attitudes which operate as a unifying force within society...

of societies . Early methods of protection involved charity
Charitable organization
A charitable organization is a type of non-profit organization . It differs from other types of NPOs in that it centers on philanthropic goals A charitable organization is a type of non-profit organization (NPO). It differs from other types of NPOs in that it centers on philanthropic goals A...

; religious organizations
Religion-supporting organization
Religious activities generally need some infrastructure to be conducted. For this reason, there generally exist religion-supporting organizations, which are some form of organization that manage:* the upkeep of places of worship, e.g...

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
Ancient Rome
Ancient Rome was a thriving civilization that grew on the Italian Peninsula as early as the 8th century BC. Located along the Mediterranean Sea and centered on the city of Rome, it expanded to one of the largest empires in the ancient world....

. 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
Social stigma
Social stigma is the severe disapproval of or discontent with a person on the grounds of characteristics that distinguish them from other members of a society.Almost all stigma is based on a person differing from social or cultural norms...

. Elementary mutual aid agreements and pensions did arise in antiquity . Early in the Roman empire
Roman Empire
The Roman Empire was the post-Republican period of the ancient Roman civilization, characterised by an autocratic form of government and large territorial holdings in Europe and around the Mediterranean....

, associations were formed to meet the expenses of burial, cremation, and monuments—precursors to burial insurance
Burial society
A burial society is a form of friendly society. These groups historically existed in England, and constituted for the purpose of providing by voluntary subscriptions, for insuring money to be paid on the death of a member, or for the funeral expenses of the husband, wife or child of a member, or of...

and friendly societies
Friendly society
A friendly society is a mutual association for insurance, pensions or savings and loan-like purposes, or cooperative banking. It is a mutual organization or benefit society composed of a body of people who join together for a common financial or social purpose...

. 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
Columbarium
A columbarium is a place for the respectful and usually public storage of cinerary urns . The term comes from the Latin columba and originally referred to compartmentalized housing for doves and pigeons .The Columbarium of Pomponius Hylas is a particularly fine ancient Roman example, rich in...

, or burial vaults, owned by the fund—the precursor to mutual insurance companies
Mutual insurance
A mutual insurance company is an insurance company which has no shareholders but instead is owned entirely by its policyholders. The primary form of financial business set up as a mutual company in the United States has been mutual insurance. Under this idea, what would have been profits are...

. Other early examples of mutual surety
Surety
A surety or guarantee, in finance, is a promise by one party to assume responsibility for the debt obligation of a borrower if that borrower defaults...

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
Compound interest
Compound interest arises when interest is added to the principal, so that from that moment on, the interest that has been added also itself earns interest. This addition of interest to the principal is called compounding...

was studied and probability theory
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...

emerged as a well understood mathematical discipline. Another important advance came in 1662 from a London draper
Draper
Draper is the now largely obsolete term for a wholesaler, or especially retailer, of cloth, mainly for clothing, or one who works in a draper's shop. A draper may additionally operate as a cloth merchant or a haberdasher. The drapers were an important trade guild...

named John Graunt
John Graunt
John Graunt was one of the first demographers, though by profession he was a haberdasher. Born in London, the eldest of seven or eight children of Henry and Mary Graunt. His father was a draper who had moved to London from Hampshire...

, who showed that there were predictable patterns of longevity and death in a defined group, or cohort
Cohort (statistics)
In statistics and demography, a cohort is a group of subjects who have shared a particular time together during a particular time span . Cohorts may be tracked over extended periods in a cohort study. The cohort can be modified by censoring, i.e...

, 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
Life table
In actuarial science, a life table is a table which shows, for each age, what the probability is that a person of that age will die before his or her next birthday...

. 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
Edmond Halley
Edmond Halley FRS was an English astronomer, geophysicist, mathematician, meteorologist, and physicist who is best known for computing the orbit of the eponymous Halley's Comet. He was the second Astronomer Royal in Britain, following in the footsteps of John Flamsteed.-Biography and career: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 premium
Insurance
In law and economics, insurance is a form of risk management primarily used to hedge against the risk of a contingent, uncertain loss. Insurance is defined as the equitable transfer of the risk of a loss, from one entity to another, in exchange for payment. An insurer is a company selling the...

or amount of money someone of a given age should pay to purchase a life-annuity .

### Early actuaries

James Dodsons’s
James Dodson
James Dodson FRS was a British mathematician, actuary and innovator in the insurance industry.-Life:Matthew Maty, in his Mémoire sur la vie et sur les écrits de M. A. de Moivre, wrote that Dodson was a pupil of Abraham de Moivre. He worked as an accountant and teacher...

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 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
Stochastic
Stochastic refers to systems whose behaviour is intrinsically non-deterministic. A stochastic process is one whose behavior is non-deterministic, in that a system's subsequent state is determined both by the process's predictable actions and by a random element. However, according to M. Kac and E...

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
Financial economics
Financial Economics is the branch of economics concerned with "the allocation and deployment of economic resources, both spatially and across time, in an uncertain environment"....

. 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
Glass–Steagall Act of 1932
The first Glass–Steagall Act was a law enacted by the United States Congress in 1932. It was the first time that currency was permitted to be allocated for the Federal Reserve System...

, the adoption of the Mandatory Security Valuation Reserve by the National Association of Insurance Commissioners
National Association of Insurance Commissioners
The National Association of Insurance Commissioners is an Internal Revenue Code Section 501 non-profit organization which seeks to organize the regulatory and supervisory efforts of the various state insurance commissioners from around the United States. The NAIC was formed in 1871. Its current...

; the latter law cushioned market fluctuations. Finally pensions valuations and funding must comply with the Financial Accounting Standards Board
Financial Accounting Standards Board
The Financial Accounting Standards Board is a private, not-for-profit organization whose primary purpose is to develop generally accepted accounting principles within the United States in the public's interest...

, (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 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
Asset allocation
Asset allocation is an investment strategy that attempts to balance risk versus reward by adjusting the percentage of each asset in an investment portfolio according to the investors risk tolerance, goals and investment time frame.-Description:...

mix of investments can change the value of liabilities and assets (by changing the discount rate
Discount rate
The discount rate can mean*an interest rate a central bank charges depository institutions that borrow reserves from it, for example for the use of the Federal Reserve's discount window....

assumption). This concept is inconsistent with financial economics
Financial economics
Financial Economics is the branch of economics concerned with "the allocation and deployment of economic resources, both spatially and across time, in an uncertain environment"....

.

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:
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. .

### 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 .

• Actuarial control cycle
Actuarial control cycle
The actuarial control cycle is a specific business activity which involves the application of actuarial science to real world business problems. Much like the accounting control cycle, the actuarial control cycle requires a professional within that field to specify a problem, develop a solution,...

• Actuarial exam
Actuarial exam
Actuarial exams are a series of professional level examinations which must be passed in order to be admitted into an actuarial society, if the society has a "membership through examination" requirement...

:Category:Actuarial associations
• Data mining
Data mining
Data mining , a relatively young and interdisciplinary field of computer science is the process of discovering new patterns from large data sets involving methods at the intersection of artificial intelligence, machine learning, statistics and database systems...

• List of actuarial topics
• Ruin theory
Ruin theory
Ruin theory, sometimes referred to as collective risk theory, is a branch of actuarial science that studies an insurer's vulnerability to insolvency based on mathematical modeling of the insurer's surplus....