Actuarial science

are professionals who are qualified in this field through examinations and experience.

Actuarial science includes a number of interrelating subjects, including probability and statistics, finance, and economics. Historically, actuarial science used deterministic models in the construction of tables and premiums. The science has gone through revolutionary changes during the last 30 years due to the proliferation of high speed computers and the synergy of stochastic actuarial models with modern financial theory ref_harvard|Frees|Frees 1990|none.

Many universities have undergraduate and graduate degree programs in actuarial science. In 2002, a Wall Street Journal survey on the best jobs in the United States listed “actuary” as the second best job ref_harvard|Lee|Lee 2002|none.

Life insurance, pensions and healthcare

Actuarial science became a formal mathematical discipline in the late 17th century with the increased demand for long-term insurance coverages such as Burial, Life insurance, and Annuities. These long term coverages required that money be set aside to pay future benefits, such as annuity and death benefits many years into the future. This requires estimating future contingent events, such as the rates of mortality by age, as well as the development of mathematical techniques for discounting the value of funds set aside and invested. This led to the development of an important actuarial concept, referred to as the Present value of a future sum. Pensions and healthcare emerged in the early 20th century as a result of collective bargaining. Certain aspects of the actuarial methods for discounting pension funds have come under criticism from modern financial economics.

* In traditional life insurance, actuarial science focuses on the analysis of mortality, the production of life tables, and the application of compound interest to produce life insurance, annuities and endowment policies. Contemporary life insurance programs have been extended to include credit and mortgage insurance, key man insurance for small businesses, long term care insurance and health savings accounts ref_harvard|Hsiao|Hsiao 2001|none.

* In health insurance, including insurance provided directly by employers, and social insurance, actuarial science focuses on the analyses of rates of disability, morbidity, mortality, fertility and other contingencies. The effects of consumer choice and the geographical distribution of the utilization of medical services and procedures, and the utilization of drugs and therapies, is also of great importance. These factors underlay the development of the Resource-Base Relative Value Scale (RBRVS) at Harvard in a multi-disciplined study. ref_harvard|Hsiao|Hsiao 1988|none Actuarial science also aids in the design of benefit structures, reimbursement standards, and the effects of proposed government standards on the cost of healthcare ref_harvard|CHBRP|cf. CHBRP 2004|none.

* In the pension industry, actuarial methods are used to measure the costs of alternative strategies with regard to the design, maintenance or redesign of pension plans. The strategies are greatly influenced by collective bargaining; the employer's old, new and foreign competitors; the changing demographics of the workforce; changes in the internal revenue code; changes in the attitude of the internal revenue service regarding the calculation of surpluses; and equally importantly, both the short and long term financial and economic trends. It is common with mergers and acquisitions that several pension plans have to be combined or at least administered on an equitable basis. When benefit changes occur, old and new benefit plans have to be blended, satisfying new social demands and various government discrimination test calculations, and providing employees and retirees with understandable choices and transition paths. Benefit plans liabilities have to be properly valued, reflecting both earned benefits for past service, and the benefits for future service. Finally, funding schemes have to be developed that are manageable and satisfy the Financial Accounting Standards Board (FASB).

* In social welfare programs, the Office of the Chief Actuary (OCACT), Social Security Administration plans and directs a program of actuarial estimates and analyses relating to SSA-administered retirement, survivors and disability insurance programs and to proposed changes in those programs. It evaluates operations of the Federal Old-Age and Survivors Insurance Trust Fund and the Federal Disability Insurance Trust Fund, conducts studies of program financing, performs actuarial and demographic research on social insurance and related program issues involving mortality, morbidity, utilization, retirement, disability, survivorship, marriage, unemployment, poverty, old age, families with children, etc., and projects future workloads. In addition, the Office is charged with conducting cost analyses relating to the Supplemental Security Income (SSI) program, a general-revenue financed, means-tested program for low-income aged, blind and disabled people. The Office provides technical and consultative services to the Commissioner, to the Board of Trustees of the Social Security Trust Funds, and its staff appears before Congressional Committees to provide expert testimony on the actuarial aspects of Social Security issues.

Actuarial science applied to other forms of insurance

Actuarial science is also applied to short-term forms of insurance, referred to as Property & Casualty or Liability insurance, or General insurance. In these forms of insurance, coverage is generally provided on a renewable annual period, (such as a yearly contract to provide homeowners insurance policy covering damage to a house and its contents for one year). Coverage can be cancelled at the end of the period by either party.

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

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

Development

Pre-formalization

In the ancient world there was no room for the sick, suffering, disabled, aged, or the poor—it was not part of the cultural consciousness of societies ref_harvard|Perkins|Perkins 1995|a. Early methods of protection involved charity; religious organizations or neighbors would collect for the destitute and needy. By the middle of the third century, 1,500 suffering people were being supported by charitable operations in Rome ref_harvard|Perkins|Perkins 1995|b. Charitable protection is still an active form of support to this very day ref_harvard|Tong1|Tong 2006|none. However, receiving charity is uncertain and is often accompanied by social stigma. Elementary mutual aid agreements and pensions did arise in antiquity ref_harvard|Thucydides|Thucydides c. 431BCE|none. 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 ref_harvard|Johnston1|Johnston 1903, §475–§476|none. 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 ref_harvard|Loan1|Loan 1992|none. However, many of these earlier forms of surety and aid would often fail due to lack of understanding and knowledge ref_harvard|FIFA2|Faculty and Institute of Actuaries 2004|a.

Initial development

The seventeenth century was a period of extraordinary advances in mathematics in Germany, France and England. At the same time there was a rapidly growing desire and need to place the valuation of personal risk on a more scientific basis. Independently from each other, compound interest was studied and probability theory emerged as a well understood mathematical discipline. Another important advance came in 1662 from a London draper named John Graunt, who showed that there were predictable patterns of longevity and death in a defined group, or cohort, of people, despite the uncertainty about the future longevity or mortality of any one individual person. This study became the basis for the original life table. It was now possible 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 (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 or amount of money someone of a given age should pay to purchase a life-annuity ref_harvard|Halley1|Halley 1693|none.

Early actuaries

James Dodson’s pioneering work on the level premium system led to the formation of the Society for Equitable Assurances on Lives and Survivorship (now commonly known as Equitable Life) in London in 1762. The company still exists, though it has 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 ref_harvard|FIFA2|Faculty and Institute of Actuaries 2004|b. 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 ref_harvard|Buhl|Bühlmann 1997 p. 166|a.

Effects of technology

In the 18th century and nineteenth centuries, computational complexity was limited to manual calculations. The actual calculations required to compute fair insurance premiums are rather complex. The actuaries of that time developed methods to construct easily-used tables, using sophisticated approximations called commutation functions, to facilitate timely, accurate, manual calculations of premiums ref_harvard|Slud1|Slud 2006|none. 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 ref_harvard|Hickman1|Hickman 2004 p. 4|none. 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 ref_harvard|Mich1|Michelbacher 1920 p. 224, 230|none. In the 1930s and 1940s, however, the rigorous mathematical foundations for stochastic processes were developed ref_harvard|Buhl|Bühlmann 1997 p. 168|b. 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 ref_harvard|MacGinnitie1|MacGinnitie 1980 p.50-51|none.

Actuarial science and modern financial economics

Some aspects of traditional actuarial science are not aligned with modern financial economics. Pension actuaries have been challenged by financial economists regarding funding and investment strategies. There are two reasons for the divergence of actuarial and financial economic practices. The first deals with the sheer complexity of calculations, and the second with the heavy burden of regulations resulting from the Armstrong investigation of 1905, the Glass-Steagal Act of 1932, the adoption of the Mandatory Security Valuation Reserve by the National Association of Insurance Commissioners; the latter law cushioned market fluctuations. Finally pensions valuations and funding must comply with the Financial Accounting Standards Board, (FASB) in the USA and Canada. The regulatory burden led to a separation of powers regarding the management and valuation of assets and liabilities.

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 ref_harvard|Whelan1|Whelan 2002|none. As a result, actuarial science developed along a different path, becoming more reliant on assumptions, as opposed to the arbitrage-free risk-neutral valuation concepts used in modern finance. The divergence is not related to the use of historical data and statistical projections of liability cash flows, but is instead caused by the manner in which traditional actuarial methods apply market data with those numbers. For example, one traditional actuarial method suggests that changing the asset allocation mix of investments can change the value of liabilities and assets (by changing the discount rate assumption). This concept is inconsistent with financial economics.

The potential of modern financial economics theory to complement existing actuarial science was recognized by actuaries in the mid-twentieth century ref_harvard|Buhl|Bühlmann 1997 p. 169–171|c. 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. ref_harvard|Darcy1|D’arcy 1989|none. Ideas from financial economics became increasingly influential in actuarial thinking, and actuarial science has started to embrace more sophisticated mathematical modelling of finance ref_harvard|Economist|"The Economist" 2006|none. 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 ref_harvard|Feld1|Feldblum 2001 p. 8–9|a. 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. ref_harvard|Moriarty|Moriarty 2006|none.

Actuaries outside insurance

There is an increasing trend to recognise that actuarial skills can be applied to a range of applications outside the insurance industry. One notable example is the use in some US states of actuarial models to set criminal sentencing guidelines. These models attempt to predict the chance of re-offending according to rating factors which include the type of crime, age, educational background and ethnicity of the offender ref_harvard|Silver|Silver and Chow-Martin 2002|none. 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 ref_harvard|Harcourt1|Harcourt 2003|none.

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 ref_harvard|Nieto|Nieto and Jung 2006 pp. 28–33|none.

ee also

* Data mining
*
* Ruin theory

External links

* [http://www.actuarialoutpost.com/actuarial_discussion_forum/forumdisplay.php?f=4 Actuarial Science Study Forum]
* [http://www.actuarialoutpost.com/actuarial-science-college-programs/ Google Map of Actuarial Science Universities in the US]
* [http://www.actuarialwiki.org Actuarial Wiki]

References

Works cited

note_label|Buhl|Bühlmann 1997 p. 166|anote_label|Buhl|Bühlmann 1997 p. 168|bnote_label|Buhl|Bühlmann 1997 p. 169–171|ccite journal
last = Bühlmann
first = Hans
year = 1997
month = November
title = THE ACTUARY: THE ROLE AND LIMITATIONS OF THE PROFESSION SINCE THE MID-19th CENTURY
journal = ASTIN Bulletin
volume = 27
issue = 2
pages = 165–171
id = ISSN|0515-0361
url = http://www.casact.org/library/astin/vol27no2/165.pdf
format = PDF
accessdate = 2006-06-28
doi = 10.1177/009385402236732

note_label|CHBRP|cf. CHBRP 2004|nonecite paper
date= February 9, 2004
url= http://www.chbrp.org/documents/hearingaids174final.pdf
format= PDF
title= Analysis of Senate Bill 174: Hearing Aids for Children
publisher= California Health Benefits Review Program
version= Revised November 19, 2004
accessdate= 2006-06-28

note_label|Darcy1|D’arcy 1989|nonecite journal
last = D’arcy
first = Stephen P.
year = 1989
month = May
title = On Becoming An Actuary of the Third Kind
journal = Proceedings of the Casualty Actuarial Society
volume = LXXVI
issue = 145
pages = 45–76
url = http://www.casact.org/pubs/proceed/proceed89/89045.pdf
format = PDF
accessdate = 2006-06-28
doi = 10.1177/009385402236732

note_label|Economist|"The Economist" 2006|nonecite web
year = 2006
url = http://www.economist.com/finance/displayStory.cfm?story_id=5436947
title = When the spinning stops: Can actuaries help to sort out the mess in corporate pensions?
accessdate = 2006-04-10
work = The Economist

note_label|Feld1|Feldblum 2001|acite book
last = Feldblum
first = Sholom
editor = Robert F. Lowe (ed.)
title = Foundations of Casualty Actuarial Science
origyear = 1990
edition = 4th
year = 2001
publisher = Casualty Actuarial Society
location = Arlington, Virginia
id = ISBN 0-9624762-2-6 LCCN|2001|0|88378
chapter = Introduction

note_label|Frees|Frees 1990|nonecite journal
last = Frees
first = Edward W.
year = 1990
month = January
title = Stochastic life contingencies with solvency considerations
journal = Transactions of the Society of Actuaries
volume = XLII
issue =
pages = 91–148
url = http://library.soa.org/library/tsa/1990-95/TSA90V427.pdf
format = PDF
accessdate = 2006-06-28
doi = 10.1177/009385402236732

note_label|Halley1|Halley 1693|nonecite journal
last = Halley
first = Edmond
authorlink = Edmond Halley
year = 1693
title = 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
journal = Philosophical Transactions of the Royal Society of London
volume = 17
pages = 596–610
url = http://www.york.ac.uk/depts/maths/histstat/halley.pdf
format = PDF
id = ISSN|0260-7085
accessdate = 2006-06-21
doi = 10.1177/009385402236732

note_label|Harcourt1|Harcourt 2003|nonecite journal
last = Harcourt
first = Bernard E.
year = 2003
title = The Shaping of Chance: Actuarial Models and Criminal Profiling at the Turn of the Twenty-First Century
journal = University of Chicago Law Review
volume = 70
issue = 105
pages = 105–128
doi = 10.2307/1600548
id = ISSN|0041-9494
url = http://www.law.uchicago.edu/faculty/harcourt/resources/08_harcourt.pdf
format = PDF
accessdate = 2007-02-06

note_label|Hickman1|Hickman 2004 p. 4|nonecite web
url = http://www.wiley.co.uk/eoas/pdfs/TAH012-.pdf
title = History of Actuarial Profession
accessdate = 2006-06-28
last = Hickman
first = James
year = 2004
format = PDF
work = Encyclopedia of Actuarial Science
publisher = John Wiley & Sons, Ltd.
pages = 4

note_label|Hsiao|Hsiao 2001|nonecite journal
last = Hsiao
first = William C.
year = 2001
month = August
title = Commentary: Behind the Ideology and Theory: What Is the Empirical Evidence for Medical Savings Accounts?
journal = Journal of Health Politics, Policy and Law
volume = 26
issue = 4
pages = 733–737
doi =10.1215/03616878-26-4-733
id =
url = http://www.hsph.harvard.edu/phcf/Papers/Ideology%20and%20theory%20-%20Hsiao.pdf
format = PDF
accessdate = 2006-07-01
pmid = 11523960

note_label|Hsiao|Hsiao 1988|nonecite web
url = http://www.hsph.harvard.edu/faculty/WilliamHsiao.html
title = Harvard School of Public Health
accessdate = 2006-06-28
last = Hsiao
first = William C
year = 2004
format = PDF

note_label|Johnston1|Johnston 1903, §475–§476|nonecite book
last = Johnston
first = Harold Whetstone
authorlink = Harold Whetstone Johnston
others = Revised by Mary Johnston
title = The Private Life of the Romans
origyear = 1903
url = http://www.forumromanum.org/life/johnston.html
accessdate = 2006-06-26
year = 1932
publisher = Scott, Foresman and Company
location = Chicago, Atlanta
id = LCCN|32|00|7692
pages = §475–§476
chapter = BURIAL PLACES AND FUNERAL CEREMONIES
chapterurl = http://www.forumromanum.org/life/johnston_14.html
quote = 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.

note_label|Lee|Lee 2002|nonecite web
last = Lee
first = Tony
year = 2002
url = http://www.careerjournal.com/jobhunting/change/20020507-lee.html
title = 2002: Rating the Nation's Best and Worst Jobs
accessdate = 2006-04-04

note_label|Loan1|Loan 1992|nonecite journal
last = Loan
first = Albert
year = 1991/92
month = Winter
title = Institutional Bases of the Spontaneous Order: Surety and Assurance
journal = Humane Studies Review
volume = 7
issue = 1
url = http://mason.gmu.edu/~ihs/w91essay.html
accessdate = 2006-06-26
doi = 10.1177/009385402236732
pages = 538

note_label|MacGinnitie1|MacGinnitie 1980 p.50-51|nonecite journal
last = MacGinnitie
first = James
year = 1980
month = November
title = The Actuary and his Profession: Growth, Development, Promise
journal = Proceedings of the Casualty Actuarial Society
volume = LXVII
issue = 127
pages = 49–56
url = http://www.casualtyactuarialsociety.com/pubs/proceed/proceed80/80049.pdf
format = PDF
accessdate = 2006-06-28
doi = 10.1177/009385402236732

note_label|Mich1|Michelbacher 1920 p. 224, 230|nonecite journal
last = Michelbacher
first = Gustav F.
year = 1920
month =
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://www.casact.org/pubs/proceed/proceed19/19201.pdf
format = PDF
accessdate = 2006-06-28
doi = 10.1177/009385402236732

note_label|Moriarty|Moriarty 2006|nonecite web
url = http://www.contingencies.org/julaug06/actuarys_new_clothes_0706.asp
title = The Actuary's New Clothes, A Canadian Perspective on the Financial Economics Debate
accessdate = 2006-06-28
last = Moriarty
first = Charlene
journal = American Academy of Actuaries, Contingencies Jul/Aug
year = 2006
format = PDF

note_label|Nieto|Nieto and Jung 2006 pp. 28–33|nonecite paper
author = Nieto, Marcus and David Jung
title = The Impact of Residency Restrictions on Sex Offenders and Correctional Management Practices: A Literature Review
publisher = California Research Bureau, California State Library
date = August 2006
url = http://www.library.ca.gov/crb/06/08/06-008.pdf
format = PDF
accessdate = 2006-09-18

note_label|Perkins|Perkins 1995|anote_label|Perkins|Perkins 1995|bcite book
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 LCCN|94|0|42650

note_label|Silver|Silver and Chow-Martin 2002|nonecite journal
last = Silver
first = Eric
coauthors = Lynette Chow-Martin
year = 2002
month = October
title = A Multiple Models Approach To Assessing Recidivism Risk: Implications for Judicial Decision Making
journal = Criminal Justice and Behavior
volume = 29
issue = 5
pages = 538–568
doi = 10.1177/009385402236732
id = ISSN|0093-8548
url = http://cjb.sagepub.com/cgi/reprint/29/5/538.pdf
format = PDF
accessdate = 2006-09-18

note_label|Slud1|Slud 2006|nonecite book
last = Slud
first = Eric V.
title = Actuarial Mathematics and Life-Table Statistics
origyear = 2001
url = http://www.math.umd.edu/~evs/s470/BookChaps/01Book.pdf
format = PDF
accessdate = 2006-06-28
year = 2006
pages = 149–150
chapter = 6: Commutation Functions, Reserves & Select Mortality
chapterurl = http://www.math.umd.edu/~evs/s470/BookChaps/Chp6.pdf
quote = 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.

note_label|Thucydides|Thucydides c. 431BCE|nonecite book
last = Thucydides
authorlink = Thucydides
others = Translated by Richard Crawley
title = The History of the Peloponnesian War
url = http://classics.mit.edu/Thucydides/pelopwar.html
accessdate = 2006-06-27
year = c. 431 BCE
location = Greece
chapter = VI - Funeral Oration of Pericles
chapterurl = http://classics.mit.edu/Thucydides/pelopwar.2.second.html
quote = 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.

note_label|Tong1|Tong 2006|nonecite news
first = Vinnee
last = Tong
url = http://www.suntimes.com/output/news/cst-nws-phil19.html
title = Americans’ donations to charity near record
work = Chicago Sun-Times
publisher = Digital Chicago Inc.
date = June 19, 2006
accessdate = 2006-06-21

note_label|Whelan1|Whelan 2002|nonecite news
first = Shane
last = Whelan
url = http://www.the-actuary.org.uk/pdfs/02_12_08.pdf
title = Actuaries’ contributions to financial economics
work = The Actuary
publisher = Staple Inn Actuarial Society
pages = 34–35
date = December 2002
accessdate = 2006-06-28
format=PDF

Bibliography

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