Information About

Actuary




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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, their reasons for being, their complexity, their mathematics, and the way they work . They 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 totally avoided, it is helpful to take measures to minimize their financial impact when they occur. These risks can impact 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 .

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 , Pension s, Mortgage and Credit Insurance , short and long term Disability , and Medical, Dental , Health Savings Account s 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 .

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 properly reflect the increasing long term risks associated with Climate Change , cultural litigiousness, Acts Of War , Terrorism and politics .

In 2002, a '''' in 2006 included actuaries among the 25 "Best Professions" that it expects will be in great demand in the future .


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. Merchant s 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 .


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 . 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 . Charitable protection is still an active form of support to this very day . However, receiving charity is uncertain and is often accompanied by Social Stigma . Elementary Mutual Aid agreements and pensions did arise in antiquity . 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 . Other early examples of mutual Surety and Assurance pacts can be traced back to various forms of fellowship within the Saxon clans of England and their Germanic forbears, and to Celtic society . However, many of these earlier forms of surety and aid would fail due to lack of understanding and knowledge .


Development of theory

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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 .


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’ . 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 . 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 .


Development of the modern profession

See Also: Actuarial science


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 . 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, rigorous mathematical foundations for Stochastic processes were developed . 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 .

Another modern development is the convergence of modern Financial Theory with actuarial science . 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 . 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 . Today, the profession, both in practice and in the educational syllabi of many actuarial organizations, combines tables, loss models, stochastic methods, and financial theory , but is still not completely aligned with modern Financial Economics .


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 , as well as 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 .


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 Distribution s and the Parameter s 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 Witness es 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 . One of the latest developments in the industry, insurance securitization, requires both the actuarial and finance skills .

Another field in which actuaries are becoming more prominent is that of Enterprise Risk Management , for both financial and non-financial corporations . 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 .


Remuneration

The credentialing and examination procedure for becoming a fully qualified actuary can be discouraging. 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 . In the UK, where there are approximately 8,000 fully qualified actuaries, typical post-university starting salaries range between GBP £24,000 and £30,000 (approx. US$ 44,000–US$55,000 c. June 2006) and newly qualified actuaries in insurance companies earn somewhere between £44,000 and £64,000 (approx. US$81,000–US$118,000 c. June 2006) per year. Many successful actuaries earn over £100,000 a year (approx. US$185,000 c. June 2006) .

In developing markets such as India , annual compensation for newly qualified actuaries starts at around 8 Lakh (800,000 Indian Rupee s or approximately US$17,500 c. June 2006) and can go as high as 20 lakh (approx. US$43,600 c. June 2006) .



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 that 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 been involved in. 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 for him or her to qualify as a “Fellow of the (Institute/Faculty) of Actuaries” (FIA/FFA) .

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 accredited programmes are currently
Heriot-Watt University , Edinburgh and City University, London . Full-time accredited
masters programmes are also Heriot-Watt and City and part-time accredited masters
degrees are offered by Imperial College , and the University Of Leicester .
Actuarial programmes that offer the possibility of exemption from individual
professional exams are also available at the London School Of Economics , University Of Southampton ,
and the University Of Kent . In the Republic of Ireland exemptions
are offered by University College Dublin and Dublin City University .


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’ membership requirements include passing six examinations for Associateship, and an additional two exams, together with the completion of a professional paper, for Fellowship . The Casualty Actuary Society requires the successful completion of seven examinations 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 .

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 . Continuing education is required after certification for all actuaries who sign statements of actuarial opinion .

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 .


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 .


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 . 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 .


Australia

The education system in Australia is divided into five parts. The first three are exam-based curricula, and the final two require a professionalism course and work experience .

Part I relies on exemptions from an accredited under-graduate degree from either Macquarie University , University Of New South Wales , University Of Melbourne or Australian National University . 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 .

Part II is the Actuarial Control Cycle and is offered by the 4 universities above .

Part III consists of 4 half-year courses of which two are compulsory and the other two allow specialization .


India

The Actuarial Society 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 .


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 . 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 full exam . Thus, thousands of hours of study time should be anticipated over several years, assuming no failures . 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 .

; 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 .

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

; 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..

;. 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 " .

; Frank Redington :Developed the Redington Immunization Theory

; .

; 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 .


FICTIONAL ACTUARIES

See Also: 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. .

;Warren Schmidt: Warren is portrayed by Jack Nicholson and is from the movie '' About Schmidt ''. The movie mostly covers Schmidt's retirement from an insurance company. Schmidt is portrayed as antisocial and unfriendly. He does not want to retire and spends his free time still working on actuarial calculations.


SEE ALSO





EXTERNAL LINKS




REFERENCES


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  First Gustav F
  Year 1920
  Title The Technique of Rate Making as Illustrated by the 1920 National Revision of Workmen's Compensations Insurance Rates
  Journal Proceedings of the Casualty Actuarial Society
  Volume VI
  Issue 14
  Pages 201–249
  Url http://wwwcasactorg/pubs/proceed/proceed19/19201pdf
  Format PDF
  Accessdate 2006-06-28



  Last Nemko
  First Marty
  Year 2006
  Url http://wwwusnewscom/usnews/biztech/best_careers_2007/
  Title Best Careers 2007
  Publisher '' US News & World Report ''
  Accessdate 2007-02-20



  First Ragnar
  Last Norberg
  Year 1990
  Title Actuarial Statistics - The European Perspective
  Booktitle International Conference on the Teaching of Statistics 3, Dunedin, New Zealand
  Publisher International Association for Statistical Education
  Location Auckland , New Zealand
  Pages 405–410
  Url http://wwwstataucklandacnz/~iase/publications/18/BOOK2/B7-2pdf
  Format PDF
  Accessdate 2006-12-14



  Last Ogborn
  First ME
  Year 1956
  Title The Professional Name of Actuary
  Journal Journal of the Institute of Actuaries
  Volume 82
  Pages 233–246
  Url http://wwwactuariesorguk/files/pdf/library/JIA-082/0233-0246pdf
  Format PDF
  Accessdate 2006-08-29



  Last Ogborn
  First ME
  Year 1973
  Month July
  Url http://wwwactuariesorguk/files/pdf/library/JIA-100/0005-0014pdf
  Title CATALOGUE OF AN EXHIBITION ILLUSTRATING THE HISTORY OF ACTUARIAL SCIENCE IN THE UNITED KINGDOM
  Format PDF
  Pages 7–8
  Publisher Faculty and Institute of Actuaries
  Accessdate 2006-06-22



  Last Perkins
  First Judith
  Title The Suffering Self Pain and Narrative Representation in the Early Christian Era
  Date August 25 , 1995
  Publisher Routledge
  Location London, England
  Id ISBN 0-415-11363-6



  Last Sieger
  First Richard
  Year 1998
  Month March
  Title What is an Actuary
  Journal Future Fellows
  Volume 4
  Issue 1
  Url http://casactorg/admissions/futfell/mar98/whatishtm
  Accessdate 2006-06-22



  Title Society of Actuaries:Basic Education Catalog
  Url http://wwwsoaorg/ccm/cms-service/stream/assetasset_id=16545070&g11nenc=UTF-8
  Format PDF
  Accessdate 2006-06-11
  Year 2006
  Publisher Society Of Actuaries
  Pages 6–7
  Chapter Admission Requirements to the SOA



  Last Slud
  First Eric V
  Title Actuarial Mathematics and Life-Table Statistics
  Origyear 2001
  Url http://wwwmathumdedu/~evs/s470/BookChaps/01Bookpdf
  Format PDF
  Accessdate 2006-06-28
  Year 2006
  Pages 149–150
  Chapter 6: Commutation Functions, Reserves & Select Mortality
  Chapterurl http://wwwmathumdedu/~evs/s470/BookChaps/Chp6pdf
  Quote <small>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</small>



  Last Stearns
  First Frank Preston
  Title Cambridge sketches
  Url http://wwwgutenbergorg/dirs/etext05/7camb10txt
  Format text
  Accessdate 2007-01-15
  Edition 1st ed
  Date 1905
  Publisher J B Lippincott Company
  Location Philadelphia , Pennsylvania
  Id
  Chapter ELIZUR WRIGHT
  Quote <small>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</small>



  Url http://wwwutbildningsuse/katalog/Linjer/46asp
  Title Aktuarieprogrammet
  Accessdate 2006-09-10
  Year 2006
  Publisher Stockholm University



  Last Thucydides
  Authorlink Thucydides
  Others Translated by Richard Crawley
  Title The History Of The Peloponnesian War
  Url http://classicsmitedu/Thucydides/pelopwarhtml
  Accessdate 2006-06-27
  Year c 431 BCE
  Location Greece
  Chapter VI - Funeral Oration of Pericles
  Chapterurl http://classicsmitedu/Thucydides/pelopwar2secondhtml
  Quote <small>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</small>



  first Vinnee
  last Tong
  url http://wwwsuntimescom/output/news/cst-nws-phil19html
  title Americans’ donations to charity near record
  work Chicago Sun-Times
  publisher Digital Chicago Inc
  date June 19 , 2006
  accessdate 2006-06-21



  author Trowbridge, Charles L
  date 1989
  url http://wwwactuarialfoundationorg/research_edu/fundamentalpdf
  format PDF
  title Fundamental Concepts of Actuarial Science
  publisher Actuarial Education and Research Fund
  version Revised Edition
  accessdate 2006-06-28



  first Shane
  last Whelan
  url http://wwwthe-actuaryorguk/pdfs/02_12_08pdf
  title Actuaries’ contributions to financial economics
  work The Actuary
  publisher Staple Inn Actuarial Society
  pages 34–35
  date December 2002
  accessdate 2006-06-28


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