Actuary

Actuary
	Damage from Hurricane Katrina. Actuaries need to estimate long-term averages of such damage in order to accurately price property insurance.
Occupation
Names	Actuary
Occupation type	Profession
Activity sectors	Insurance, Reinsurance, Pension plans, Social welfare programs
Description
Competencies	Mathematics, analytical skills, business knowledge
Education required	See Credentialing and exams
Fields of; employment	Insurance companies, consulting firms, government
Related jobs	Underwriter

An actuary is a business professional who deals with the financial impact of risk and uncertainty. Actuaries have a deep understanding of financial security systems, with a focus on their complexity, their mathematics, and their mechanisms Template:Ref harvard.

Actuaries evaluate the likelihood of events and quantify the contingent outcomes in order to minimize losses, both emotional and financial, associated with uncertain undesirable events. Since many events, such as death, cannot be avoided, it is helpful to take measures to minimize their financial impact when they occur. These risks can affect both sides of the balance sheet, and require asset management, liability management, and valuation skills. Analytical skills, business knowledge and understanding of human behavior and the vagaries of information systems are required to design and manage programs that control risk Template:Ref harvard.

In 2002 and 2009, 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 Template:Ref harvard, Template:Ref harvard. The survey used six key criteria to rank jobs: environment, income, employment outlook, physical demands, security and stress. A similar survey 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 Template:Ref harvard.

Disciplines

Actuaries' insurance disciplines may be classified as life; health; pensions, annuities, and asset management; social welfare programs; property; casualty; general insurance; and reinsurance. Life, health, and pension actuaries deal with mortality risk, morbidity, and consumer choice regarding the ongoing utilization of drugs and medical services risk, and investment risk. Products prominent in their work include life insurance, annuities, pensions, mortgage and credit insurance, short and long term disability, and medical, dental, health savings accounts and long term care insurance. In addition to these risks, social insurance programs are greatly influenced by public opinion, politics, budget constraints, changing demographics and other factors such as medical technology, inflation and cost of living considerations Template:Ref harvard.

Casualty actuaries, also known as non-life or general insurance actuaries, deal with catastrophic, unnatural risks that can occur to people or property. Products prominent in their work include auto insurance, homeowners insurance, commercial property insurance, workers’ compensation, title insurance, malpractice insurance, products liability insurance, directors and officers liability insurance, environmental and marine insurance, terrorism insurance and other types of liability insurance. Reinsurance products have to accommodate all of the previously mentioned products, and in addition have to reflect properly the increasing long term risks associated with climate change, cultural litigiousness, acts of war, terrorism and politics Template:Ref harvard.

History

Need for insurance

The basic requirements of communal interests gave rise to risk sharing since the dawn of civilization. For example, people who lived their entire lives in a camp had the risk of fire, which would leave their band or family without shelter. After basic exchange came into existence, more complex forms developed beyond a basic barter economy, and new forms of risk manifested. Merchants embarking on trade journeys bore the risk of losing goods entrusted to them, their own possessions, or even their lives. Intermediaries developed to warehouse and trade goods, and they often suffered from financial risk. The primary providers in any extended families or household always ran the risk of premature death, disability or infirmity, leaving their dependents to starve. Credit procurement was difficult if the lender worried about repayment in the event of the borrower's death or infirmity. Alternatively, people sometimes lived too long, exhausting their savings, if any, or becoming a burden on others in the extended family or society Template:Ref harvard.

Early attempts

In the ancient world there was not always room for the sick, suffering, disabled, aged, or the poor—these were often not part of the cultural consciousness of societies Template:Ref harvard. Early methods of protection, aside from the normal support of the extended family, 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 Template:Ref harvard. Charitable protection is still an active form of support to this very day Template:Ref harvard. However, receiving charity is uncertain and is often accompanied by social stigma. Elementary mutual aid agreements and pensions did arise in antiquity Template:Ref harvard. 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 Template:Ref harvard. 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 Template:Ref harvard. However, many of these earlier forms of surety and aid would fail due to lack of understanding and knowledge Template:Ref harvard.

Development of theory

File:Excerpt from CDC 2003 Table 1.png

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

The 17th 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 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. In addition to constructing his own life table, Halley demonstrated a method of using his life table to calculate the premium someone of a given age should pay to purchase a life-annuity Template:Ref harvard.

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. This was the first life insurance company to use premium rates which were calculated scientifically for long-term life policies, using Dodson’s work. The company still exists, though it has run into difficulties recently. After Dodson’s death in 1757, Edward Rowe Mores took over the leadership of the group that eventually became the Society for Equitable Assurances in 1762. It was he who specified that the chief official should be called an ‘actuary’ Template:Ref harvard. Previously, the use of the term had been restricted to an official who recorded the decisions, or ‘acts’, of ecclesiastical courts, in ancient times originally the secretary of the Roman senate, responsible for compiling the Acta Senatus Template:Ref harvard. 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 Template:Ref harvard.

Development of the modern profession

In the eighteenth and nineteenth centuries, computational complexity was limited to manual calculations. The actual calculations required to compute fair insurance premiums are rather complex. The actuaries of that time developed methods to construct easily-used tables, using sophisticated approximations called commutation functions, to facilitate timely, accurate, manual calculations of premiums Template:Ref harvard. 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 Template:Ref harvard. 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. In the United States, the 1920 revision to workers' compensation rates took over two months of around-the-clock work by day and night teams of actuaries Template:Ref harvard. In the 1930s and 1940s, however, rigorous mathematical foundations for stochastic processes were developed Template:Ref harvard. Actuaries could now begin to forecast losses using models of random events instead of deterministic methods. Computers further revolutionized the actuarial profession. From pencil-and-paper to punchcards to microcomputers, the modeling and forecasting ability of the actuary has grown exponentially Template:Ref harvard.

Another modern development is the convergence of modern financial theory with actuarial science Template:Ref harvard. 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 Template:Ref harvard. However, 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 Template:Ref harvard. Today, the profession, both in practice and in the educational syllabi of many actuarial organizations, combines tables, loss models, stochastic methods, and financial theory Template:Ref harvard, but is still not completely aligned with modern financial economics (Bader & Gold 2003, pp. 1–39).

Responsibilities

Actuaries use skills in mathematics, economics, finance, probability and statistics, and business to help businesses assess the risk of certain events occurring and to formulate policies that minimize the cost of that risk. For this reason, actuaries are essential to the insurance and reinsurance industry, either as staff employees or as consultants; to other businesses, including sponsors of pension plans; and to government agencies such as the Government Actuary’s Department in the UK or the Social Security Administration in the US. Actuaries assemble and analyze data to estimate the probability and likely cost of the occurrence of an event such as death, sickness, injury, disability, or loss of property. Actuaries also address financial questions, including those involving the level of pension contributions required to produce a certain retirement income and the way in which a company should invest resources to maximize its return on investments in light of potential risk. Using their broad knowledge, actuaries help design and price insurance policies, pension plans, and other financial strategies in a manner which will help ensure that the plans are maintained on a sound financial basis Template:Ref harvard.

Traditional employment

On both the life and casualty sides, the classical function of actuaries is to calculate premiums and reserves for insurance policies covering various risks. Premiums are the amount of money the insurer needs to collect from the policyholder in order to cover the expected losses, expenses, and a provision for profit. Reserves are provisions for future liabilities and indicate how much money should be set aside now to reasonably provide for future payouts. If you inspect the balance sheet of an insurance company, you will find that the liability side consists mainly of reserves.

On the casualty side, this analysis often involves quantifying the probability of a loss event, called the frequency, and the size of that loss event, called the severity. Further, the amount of time that occurs before the loss event is also important, as the insurer will not have to pay anything until after the event has occurred. On the life side, the analysis often involves quantifying how much a potential sum of money or a financial liability will be worth at different points in the future. Since neither of these kinds of analysis are purely deterministic processes, stochastic models are often used to determine frequency and severity distributions and the parameters of these distributions. Forecasting interest yields and currency movements also plays a role in determining future costs, especially on the life side.

Actuaries do not always attempt to predict aggregate future events. Often, their work may relate to determining the cost of financial liabilities that have already occurred, called retrospective reinsurance, or the development or re-pricing of new products.

Actuaries also design and maintain products and systems. They are involved in financial reporting of companies’ assets and liabilities. They must communicate complex concepts to clients who may not share their language or depth of knowledge. Actuaries work under a strict code of ethics that covers their communications and work products, but their clients may not adhere to those same standards when interpreting the data or using it within different kinds of businesses.

Non-traditional employment

Many actuaries are general business managers or financial officers. They analyze prospective business prospects with their financial skills in valuing or discounting risky future cash flows, and many apply their pricing expertise from insurance to other lines of business. Some actuaries act as expert witnesses by applying their analysis in court trials to estimate the economic value of losses such as lost profits or lost wages.

There has been a recent widening of the scope of the actuarial field to include investment advice and asset management. Further, there has been a convergence from the financial fields of risk management and quantitative analysis with actuarial science. Now, actuaries also work as risk managers, quantitative analysts, or investment specialists. Even actuaries in traditional roles are now studying and using the tools and data previously in the domain of finance Template:Ref harvard. One of the latest developments in the industry, insurance securitization, requires both the actuarial and finance skills Template:Ref harvard.

Another field in which actuaries are becoming more prominent is that of Enterprise Risk Management, for both financial and non-financial corporations Template:Ref harvard. For example, the Basel II accord for financial institutions, and its analogue, the Solvency II accord for insurance companies, requires such institutions to account for operational risk separately and in addition to credit, reserve, asset, and insolvency risk. Actuarial skills are well suited to this environment because of their training in analyzing various forms of risk, and judging the potential for upside gain, as well as downside loss associated with these forms of risk Template:Ref harvard.

Remuneration

The credentialing and examination procedure for becoming a fully qualified actuary can be intensely demanding. Consequently, the profession remains very small throughout the world. As a result, actuaries are in high demand, and they are highly paid for the services they render Template:Ref harvard. In the UK, where there are approximately 8,000 fully qualified actuaries, typical post-university starting salaries range between GBP £25,300 and £35,000 (approx. US$50,100–US$69,300 c. January 2008) and newly qualified actuaries in insurance companies earn somewhere between £46,000 and £55,000 (approx. US$91,100–US$108,900 c. January 2008) per year. Many successful actuaries earn over £100,000 a year (approx. US$198,000 c. January 2008). These reflect nationwide salaries and numbers are likely to be higher in London or in the South East of England Template:Ref harvard.

Credentialing and exams

Becoming a fully credentialed actuary requires passing a rigorous series of exams, usually taking several years. In some countries, such as France, most study takes place in a university setting. In others, such as the U.S. and the UK, most study takes place during employment.

UK and Republic of Ireland

Qualification in the United Kingdom and the Republic of Ireland consists of a combination of exams and courses provided by the professional bodies: the Institute of Actuaries based in London, England, and the Faculty of Actuaries based in Edinburgh, Scotland — separate but coinciding bodies. No geographic limitations exist for these bodies. Students and actuaries in any part of the UK or the Republic of Ireland may be a member of either or both bodies. The exams may only be taken upon having officially joined the body, unlike many other countries where exams may be taken earlier. However, a candidate may offer proof of having previously covered topics, usually while at university, in order to be exempt from taking certain subjects. The exams themselves are now split into four sections: Core Technical (CT), Core Applications (CA), Specialist Technical (ST), and Specialist Applications (SA). For students who joined the Profession after June 2004, a further requirement that the student carry out a "Work-based skills" exercise has been brought into effect. This involves the student submitting a series of essays to the Profession detailing the work that he or she has performed. In addition to exams, essays and courses, it is required that the candidate have at least three years' experience of actuarial work under supervision of a recognized actuary in order to qualify as a Fellow of the Institute of Actuaries (FIA) or of the Faculty of Actuaries (FFA) Template:Ref harvard.

Actuaries can also gain partial credit towards Fellowship of either the Faculty or Institute of Actuaries by following an actuarial science degree at an accredited university. At the undergraduate level the only locally accredited programmes are currently at Queen's University Belfast, Heriot-Watt University, Edinburgh, the London School of Economics, University of Southampton , City University, London and the University of Kent. Full-time accredited masters programmes are provided only by the University of Kent, Heriot-Watt University and City University; part-time accredited masters degrees are offered by Imperial College London and the University of Leicester. Actuarial programmes that offer the possibility of exemption from individual professional exams are also available at City University, London, Heriot-Watt University, the London School of Economics, the University of Southampton, the University of Wales, Swansea, the University of Kent and the University of Warwick. In the Republic of Ireland exemptions are offered by National University of Ireland, Galway, Dublin City University, University College Cork and University College Dublin. Some South African universities are also accredited by the Faculty and Institute of Actuaries. These universities include the University of Cape Town, Stellenbosch University, University of the Free State and the University of the Witwatersrand.

United States

In the U.S., for life, health, and pension actuaries, exams are given by the Society of Actuaries, while for property and casualty actuaries the exams are administered by the Casualty Actuarial Society. The Society of Actuaries’ requirements for Associateship include passing five preliminary examinations, demonstrating educational experience in economics, corporate finance and applied statistics—called validation by educational experience (VEE), completing an eight-module self-learning series, and taking a course on professionalism. For Fellowship, three other modules, two exams, and a special fellowship admission course is added Template:Ref harvard. The Casualty Actuary Society requires the successful completion of seven examinations and VEE for Associateship and two additional exams for Fellowship. In addition to these requirements, casualty actuarial candidates must also complete professionalism education and be recommended for membership by existing members Template:Ref harvard.

In order to sign statements of actuarial opinion, however, American actuaries must be members of the American Academy of Actuaries. Academy membership requirements include membership in one of the recognized actuarial societies, at least three years of full-time equivalent experience in responsible actuarial work, and either residency in the United States for at least three years or a non-resident or new resident who meets certain requirements (AAA 2008a, pp. 67–68). Continuing education is required after certification for all actuaries who sign statements of actuarial opinion (AAA 2008b, pp. 5–8).

In the pension area, American actuaries must pass three examinations to become an Enrolled Actuary. Some pension-related filings to the Internal Revenue Service and the Pension Benefit Guaranty Corporation require the signature of an Enrolled Actuary. Many Enrolled Actuaries belong to the Conference of Consulting Actuaries or the American Society of Pension Professionals and Actuaries.

Canada

The Canadian Institute of Actuaries (the CIA) recognizes fellows of both the Society of Actuaries and the Casualty Actuary Society, provided that they have specialized study in Canadian actuarial practice. For fellows of the SOA, this is fulfilled by taking the CIA’s Practice Education Course (PEC). For fellows of the Casualty Actuarial Society, this is fulfilled by taking exam 7C (Canada) instead of exam 7US. Unlike their American counterparts, the CIA only has one class of actuary—Fellow. Further, the CIA requires three years of actuarial practice within the previous decade, and 18 months of Canadian actuarial practice within the last three years, to become a fellow Template:Ref harvard.

Sweden

Actuarial training in Sweden takes place at Stockholm University. The four-year master's program covers the subjects mathematics, mathematical statistics, insurance mathematics, financial mathematics, insurance law and insurance economics. The program operates under the Division of Mathematical Statistics Template:Ref harvard.

Denmark

In Denmark it normally takes five years of study at the University of Copenhagen to become an actuary with no professional experience requirement. There is a focus on statistics and probability theory, and a requirement for a master's thesis Template:Ref harvard. By Danish law, responsibility for the practise of any life insurance business must be taken by a formally acknowledged and approved actuary. In order to be approved as a formally responsible actuary, three to five years of professional experience is required Template:Ref harvard.

Australia

The education system in Australia is divided into three parts. The first part is exam-based curricula, and the final two require a professionalism course and work experience Template:Ref harvard. The system is governed by the Institute of Actuaries of Australia.

Part I relies on exemptions from an accredited under-graduate degree from either Macquarie University, University of New South Wales, University of Melbourne, Australian National University or Curtin University Template:Ref harvard. The courses would cover subjects including finance, financial mathematics, economics, contingencies, demography, models, probability and statistics. Students may also gain exemptions by passing the exams of the Institute of Actuaries in London Template:Ref harvard.

Part II is the Actuarial Control Cycle and is offered by the first four universities above Template:Ref harvard.

Part III consists of four half-year courses of which two are compulsory and the other two allow specialization Template:Ref harvard.

Greece

In Greece the only specialized school of actuaries is the Department of Statistics and Actuary-Finance Mathematics of the University of the Aegean, in Samos. The duration of studies is four years, with a practice period included, and the certificate given is a Bachelor's Degree. The Diploma of Actuary is given by the Actuaries Union of Greece, after successful exams within the Union. Other schools that offer actuary directions can be found throughout the rest departments of Statistics in the various universities of the country, most notably that of the Athens University of Economics and Business (OPA/ASOEE), which is also the top economic university of Greece.

Germany

The current rules for the German Actuarial Society require an actuary to pass more than 13 exams Template:Ref harvard.

India

The Actuarial Society of India (now converted into Institute of Actuaries of India) offers both associateship and fellowship classes of membership. However, prospective candidates must be admitted to the society as students before they achieve associateship or fellowship. The exam sequence is similar to the British model, with Core and Specialty technical and application exams. The exams are conducted twice a year during the months of May-June and October-November Template:Ref harvard.

South Africa

Actuaries in South Africa are served by the Actuarial Society of South Africa (ASSA). Until recently the requirement to qualify as an actuary in South Africa was to pass the exams hosted by the UK bodies. Starting in 2010 a South African actuarial qualification hosted by ASSA will replace this arrangement. ASSA's website

Other countries

Many other countries pattern their requirements after the larger societies of the US or UK. In general, the websites of these organizations are often the easiest source for finding out about membership requirements.

Exam support

As these qualifying exams are rigorous, support is usually available to people progressing through the exams. Often, employers provide paid on-the-job study time and paid attendance at seminars designed for the exams Template:Ref harvard. Also, many companies which employ actuaries have automatic pay raises or promotions when exams are passed. As a result, actuarial students have strong incentives for devoting adequate study time during off-work hours. A common rule of thumb for exam students is that roughly 400 hours of study time are necessary for each four-hour exam Template:Ref harvard. Thus, thousands of hours of study time should be anticipated over several years, assuming no failures Template:Ref harvard. In practice, as the historical passing percentages remain below 50% for these exams, the “travel time” to credentialing is extended and more study time is needed. This process resembles formal schooling, so that actuaries who are sitting for exams are still called “students” or “candidates” despite holding important positions with substantial responsibilities.

Notable actuaries

James Dodson: Head of the Royal Mathematical School, and Stone's School, Dodson built on the statistical mortality tables developed by Edmund Halley in 1693 Template:Ref harvard.

Edmond Halley: While Halley actually predated much of what is now considered the start of the actuarial profession, he was the first to mathematically and statistically rigorously calculate premiums for a life insurance policy Template:Ref harvard.

James C. Hickman: Notable actuarial educator, researcher, and author Template:Ref harvard.

Edward Rowe Mores: First person to use the title ‘actuary’ with respect to a business position Template:Ref harvard.

William Morgan: Morgan was the appointed Actuary of the Society for Equitable Assurances in 1775. He expanded on Mores's and Dodson's work, and may be rightly considered the father of the actuarial profession in that his title became applied to the field as a whole.Template:Ref harvard.

Maurice Princet: French actuary and close associate of artist Pablo Picasso. Princet is considered "Le Mathématicien du Cubisme" ("The Mathematician of Cubism") for his "critical influence on Picasso’s development as an artist at the birth of cubism" Template:Ref harvard.

Frank Redington: Developed the Redington Immunization Theory

Isaac M. Rubinow: Founder and first president of the Casualty Actuarial Society Template:Ref harvard.

Elizur Wright: American actuary and abolitionist, professor of mathematics at Western Reserve College (Ohio). He campaigned for laws that required life insurance companies to hold sufficient reserves to guarantee that policies would be paid Template:Ref harvard.

David X. Li: a Canadian qualified actuary who in the early 2000s pioneered the use of Gaussian copula models for the pricing of collateralized debt obligations (CDOs).[2][3] The Financial Times called him "the world’s most influential actuary," [1] while in the aftermath of the Global financial crisis of 2008–2009, to which Li's model has been credited partly to blame,[2][1] his model has been called a "recipe for disaster".

Fictional actuaries

Due to the low public-profile of the job, some of the most recognisable actuaries to the general public happen to be characters in movies. Many actuaries were unhappy with the stereotypical portrayals of these actuaries as unhappy, math-obsessed and socially inept people; others have claimed that the portrayals are close to home, if a bit exaggerated. Template:Ref harvard.

References

AAA (2008a), American Academy of Actuaries: 2008 Yearbook (PDF), Washington, DC: American Academy of Actuaries, pp. 67–68, retrieved 2008-09-14

AAA (2008b), Qualification Standards for Actuaries Issuing Statements of Actuarial Opinion in the United States (PDF), Washington, DC: American Academy of Actuaries, pp. 5–8, retrieved 2008-09-14

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Bader, Lawrence N.; Gold, Jeremy (January 2003), "Reinventing Pension Actuarial Science" (PDF), Pension Forum, vol. 14, no. 2, pp. 1–39, retrieved 2008-09-14

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^{^} Boyle, Phelim (2002). "The actuary and the artist" (PDF). The Actuary: 32. Retrieved 2007-03-15. {{cite journal}}: Unknown parameter |month= ignored (help)

^a ^b ^c Bühlmann, Hans (1997). "The actuary: The role and limitations of the profession since the mid-19th century" (PDF). ASTIN Bulletin. 27 (2): 165–171. ISSN 0515-0361. Retrieved 2006-06-28. {{cite journal}}: Unknown parameter |month= ignored (help)

^a ^b ^c "Actuaries". Occupational Outlook Handbook 2008-09 Edition. U.S. Department of Labor, Bureau of Labor Statistics. 2007-12-18. Retrieved 2008-09-14.

^{^} "2008 CAS Basic Education Summary" (PDF). Syllabus of Basic Education. Casualty Actuarial Society. 2008. Retrieved 2008-01-11.

^{^} "History". CAS Overview. Casualty Actuarial Society. 2008. Retrieved 2008-09-14.

^{^} Chaptman, Dennis (2006-09-13). "James C. Hickman, former business school dean, dies". News. University of Wisconsin-Madison. Retrieved 2008-01-11.

^{^} "Membership & Education: Canadian Enrollment Information". Canadian Institute of Actuaries. 2004. Retrieved 2006-06-11. {{cite web}}: Unknown parameter |month= ignored (help)

^{^} Coleman, Lynn G. (2003). "Was "About Schmidt" about actuaries?". The Future Actuary. 12 (1). Retrieved 2006-08-29. {{cite journal}}: Unknown parameter |month= ignored (help)

^{^} D’arcy, Stephen P. (1989). "On Becoming An Actuary of the Third Kind" (PDF). Proceedings of the Casualty Actuarial Society. LXXVI (145): 45–76. Retrieved 2006-06-28. {{cite journal}}: Unknown parameter |month= ignored (help)

^{^} D’arcy, Stephen P. (2005). "On Becoming An Actuary of the Fourth Kind" (PDF). Proceedings of the Casualty Actuarial Society. XCII (177): 745–754. Retrieved 2007-07-05. {{cite journal}}: Unknown parameter |month= ignored (help)

^{^} "Inhalte der Ausbildung zum/zur Aktuar/in DAV" (in Template:De icon see here for Google translation). German Actuarial Society. 2006. Retrieved 2008-09-28. {{cite web}}: External link in |language= (help)CS1 maint: unrecognized language (link)

^{^} Lomas, Anna (2007-02-26). "Occupational profile: Actuary, consultancy" (PDF). AGCAS. p. 4. Retrieved 2008-01-28.

^{^} "Actuary Salary Survey". D. W. Simpson & Company. 2006. Retrieved 2006-06-11.

^a ^b Feldblum, Sholom (2001) [1990]. "Introduction". In Robert F. Lowe (ed.) (ed.). Foundations of Casualty Actuarial Science (4th ed.). Arlington, Virginia: Casualty Actuarial Society. ISBN [[Special:BookSources/0-9624762-2-6 LCCN 20-1 – 0|0-9624762-2-6 [[LCCN (identifier)|LCCN]] [https://www.loc.gov/item/20000001 20-1] – 0]]. {{cite book}}: |editor= has generic name (help); Check |isbn= value: invalid character (help); External link in |isbn= (help)

^a ^b ^c ^d "History of the actuarial profession". Faculty and Institute of Actuaries. 2004-01-13. Retrieved 2008-11-12.

^{^} "How do I become a student?". Actuarial Profession. Faculty and Institute of Actuaries. 2006. Retrieved 2008-11-12.

^{^} Halley, Edmond (1693). "An Estimate of the Degrees of the Mortality of Mankind, Drawn from Curious Tables of the Births and Funerals at the City of Breslaw; With an Attempt to Ascertain the Price of Annuities upon Lives" (PDF). Philosophical Transactions of the Royal Society of London. 17: 596–610. doi:10.1098/rstl.1693.0007. ISSN 0260-7085. Retrieved 2006-06-21.

^{^} Haastrup, Svend and Jens Perch Nielsen. "The historical perspective of the Danish actuarial profession" (PDF). Retrieved 2006-12-14. {{cite journal}}: Cite journal requires |journal= (help)

^{^} Hickman, James (2004). "History of Actuarial Profession" (PDF). Encyclopedia of Actuarial Science. John Wiley & Sons, Ltd. p. 4. Retrieved 2006-06-28.

^{^} "Education". Institute of Actuaries of Australia. 2006. Retrieved 2007-05-01.

^a ^b "Part I". Courses. Institute of Actuaries of Australia. 2006. Retrieved 2007-05-01.

^{^} "Part II (Actuarial Control Cycle)". Courses. Institute of Actuaries of Australia. 2006. Retrieved 2007-05-01.

^{^} "Part III". Courses. Institute of Actuaries of Australia. 2006. Retrieved 2007-05-01.

^{^} Johnston, Harold Whetstone (1932) [1903]. "Burial places and funeral ceremonies". The Private Life of the Romans. Revised by Mary Johnston. Chicago, Atlanta: Scott, Foresman and Company. pp. §475–§476. LCCN 32-0 – 00. Retrieved 2006-06-26. Early in the Empire, associations were formed for the purpose of meeting the funeral expenses of their members, whether the remains were to be buried or cremated, or for the purpose of building columbāria, or for both.…If the members had provided places for the disposal of their bodies after death, they now provided for the necessary funeral expenses by paying into the common fund weekly a small fixed sum, easily within the reach of the poorest of them. When a member died, a stated sum was drawn from the treasury for his funeral .... If the purpose of the society was the building of a columbārium, the cost was first determined and the sum total divided into what we should call shares (sortēs virīlēs), each member taking as many as he could afford and paying their value into the treasury. {{cite book}}: External link in |chapterurl= (help); Unknown parameter |chapterurl= ignored (|chapter-url= suggested) (help)

^{^} Krutov, Alex (2006). "Insurance Linked Securities". Financial Engineering News magazine (48). Retrieved 2006-11-30.

^{^} Lee, Tony (2002). "2002: Rating the Nation's Best and Worst Jobs". Retrieved 2006-04-04.

^{^} Loan, Albert (1991/92). "Institutional Bases of the Spontaneous Order: Surety and Assurance". Humane Studies Review. 7 (1). Retrieved 2006-06-26. {{cite journal}}: Check date values in: |year= (help); Unknown parameter |month= ignored (help)

^{^} MacGinnitie, James (1980). "The Actuary and his Profession: Growth, Development, Promise" (PDF). Proceedings of the Casualty Actuarial Society. LXVII (127): 49–56. Retrieved 2006-06-28. {{cite journal}}: Unknown parameter |month= ignored (help)

^{^} Michelbacher, Gustav F. (1920). "The Technique of Rate Making as Illustrated by the 1920 National Revision of Workmen's Compensations Insurance Rates" (PDF). Proceedings of the Casualty Actuarial Society. VI (14): 201–249. Retrieved 2006-06-28. {{cite journal}}: Cite has empty unknown parameter: |month= (help)

^{^} Nemko, Marty (2006). "Best Careers 2007". U.S. News & World Report. Archived from the original on 2007-12-26. Retrieved 2008-09-14. {{cite web}}: |archive-date= / |archive-url= timestamp mismatch; 2007-11-18 suggested (help)

^{^} Needleman, Sarah (2009). "Doing the Math to Find the Good Jobs". Wall Street Journal. Retrieved 2009-01-12.

^{^} Norberg, Ragnar (1990). "Actuarial Statistics - The European Perspective" (PDF). International Conference on the Teaching of Statistics 3, Dunedin, New Zealand. Auckland, New Zealand: International Association for Statistical Education. pp. 405–410. Retrieved 2006-12-14. {{cite conference}}: Unknown parameter |booktitle= ignored (|book-title= suggested) (help)

^a ^b Ogborn, M.E. (1956). "The Professional Name of Actuary" (PDF). Journal of the Institute of Actuaries. 82: 233–246. Retrieved 2008-11-12.

^{^} Ogborn, M.E. (1973). "Catalogue of an exhibition illustrating the history of actuarial science in the United Kingdom" (PDF). Faculty and Institute of Actuaries. pp. 7–8. Retrieved 2008-11-12. {{cite web}}: Unknown parameter |month= ignored (help)

^a ^b Perkins, Judith (1995-08-25). The Suffering Self; Pain and Narrative Representation in the Early Christian Era. London, England: Routledge. ISBN [[Special:BookSources/0-415-11363-6 LCCN 94-0 – 0|0-415-11363-6 [[LCCN (identifier)|LCCN]] [https://www.loc.gov/item/94000000 94-0] – 0]]. {{cite book}}: Check |isbn= value: invalid character (help); External link in |isbn= (help)

^{^} Sieger, Richard (1998). "What is an Actuary?". Future Fellows. 4 (1). Retrieved 2006-06-22. {{cite journal}}: Unknown parameter |month= ignored (help)

^{^} "Admission Requirements to the SOA". Spring 2008 Basic Education Catalog. Society of Actuaries. 2008. Retrieved 2008-01-11.

^{^} Slud, Eric V. (2006) [2001]. "6: Commutation Functions, Reserves & Select Mortality". Actuarial Mathematics and Life-Table Statistics (PDF). pp. 149–150. Retrieved 2006-06-28. The Commutation Functions are a computational device to ensure that net single premiums ... can all be obtained from a single table lookup. Historically, this idea has been very important in saving calculational labor when arriving at premium quotes. Even now…company employees without quantitative training could calculate premiums in a spreadsheet format with the aid of a life table. {{cite book}}: External link in |chapterurl= (help); Unknown parameter |chapterurl= ignored (|chapter-url= suggested) (help)

^{^} Stearns, Frank Preston (1905). "Elizur Wright". Cambridge sketches (text) (1st ed.). Philadelphia, Pennsylvania: J. B. Lippincott Company. LCCN 05-0 – 0. Retrieved 2007-01-15. This danger could only be averted by placing their rates of insurance on a scientific basis, which should be the same and unalterable for all companies. ... After two or three interviews with Elizur Wright the presidents of the companies came to the conclusion that he was exactly the man that they wanted, and they commissioned him to draw up a revised set of tables and rates which could serve them for a uniform standard. {{cite book}}: Cite has empty unknown parameter: |chapterurl= (help)

^{^} "Aktuarieprogrammet" (in Template:Sv icon). Stockholm University. 2006. Retrieved 2006-09-10.{{cite web}}: CS1 maint: unrecognized language (link)

^{^} Thucydides (c. 431 BCE). "VI - Funeral Oration of Pericles". [[The History of the Peloponnesian War]]. Translated by Richard Crawley. Greece. Retrieved 2006-06-27. My task is now finished. ... those who are here interred have received part of their honours already, and for the rest, their children will be brought up till manhood at the public expense: the state thus offers a valuable prize, as the garland of victory in this race of valour, for the reward both of those who have fallen and their survivors. {{cite book}}: Check date values in: |year= (help); External link in |chapterurl= (help); URL–wikilink conflict (help); Unknown parameter |chapterurl= ignored (|chapter-url= suggested) (help)

^{^} Tong, Vinnee (2006-06-19). "Americans' donations to charity near record". Chicago Sun-Times. Digital Chicago Inc. Retrieved 2006-06-21.

^{^} Trowbridge, Charles L. (1989). "Fundamental Concepts of Actuarial Science" (PDF). Revised Edition. Actuarial Education and Research Fund. Retrieved 2006-06-28. {{cite journal}}: Cite journal requires |journal= (help)

^{^} Whelan, Shane (December 2002). "Actuaries' contributions to financial economics" (PDF). The Actuary. Staple Inn Actuarial Society. pp. 34–35. Retrieved 2006-06-28.

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