Category: Actuarial science

Annuities in the European Union
Under European Union law, an annuity is a financial contract which provides an income stream in return for an initial payment with specific parameters. It is the opposite of a settlement funding. A Sw
Retirement spend-down
At retirement, individuals stop working and no longer get employment earnings, and enter a phase of their lives, where they rely on the assets they have accumulated, to supply money for their spending
In simple terms, risk is the possibility of something bad happening. Risk involves uncertainty about the effects/implications of an activity with respect to something that humans value (such as health
Life expectancy
Life expectancy is a statistical measure of the average time an organism is expected to live, based on the year of its birth, current age, and other demographic factors like sex. The most commonly use
Pension regulation
Pension regulation is a legal term encompassing, the set of laws, rules and authoritative standards governing the pension industry, and the procedures needed to enforce them. Pension regulation varies
Bühlmann model
In credibility theory, a branch of study in actuarial science, the Bühlmann model is a random effects model (or "variance components model" or hierarchical linear model) used to determine the appropri
Statutory reserve
In the business of insurance, statutory reserves are those assets an insurance company is legally required to maintain on its balance sheet with respect to the unmatured obligations (i.e., expected fu
Office of the Chief Actuary
The Office of the Chief Actuary is a government agency that has responsibility for actuarial estimates regarding social welfare programs. In Canada, the Office of the Chief Actuary works with the Cana
IFRS 17 is an International Financial Reporting Standard that was issued by the International Accounting Standards Board in May 2017. It will replace IFRS 4 on accounting for insurance contracts and h
Influential observation
In statistics, an influential observation is an observation for a statistical calculation whose deletion from the dataset would noticeably change the result of the calculation. In particular, in regre
Life annuity
A life annuity is an annuity, or series of payments at fixed intervals, paid while the purchaser (or annuitant) is alive. The majority of life annuities are insurance products sold or issued by life i
Liability-driven investment strategy
Liability-driven investment policies and asset management decisions are those largely determined by the sum of current and future liabilities attached to the investor, be it a household or an institut
Medical underwriting
Medical underwriting is a health insurance term referring to the use of medical or health information in the evaluation of an applicant for coverage, typically for life or health insurance. As part of
Reinsurance to close
Reinsurance to close (RITC) is a business transaction whereby the estimated future liabilities of an insurance company are reinsured into another, in order that the profitability of the former can be
Computational finance
Computational finance is a branch of applied computer science that deals with problems of practical interest in finance. Some slightly different definitions are the study of data and algorithms curren
Actuarial present value
The actuarial present value (APV) is the expected value of the present value of a contingent cash flow stream (i.e. a series of payments which may or may not be made). Actuarial present values are typ
Panjer recursion
The Panjer recursion is an algorithm to compute the probability distribution approximation of a compound random variablewhere both and are random variables and of special types. In more general cases
Compound annual growth rate
Compound annual growth rate (CAGR) is a business and investing specific term for the geometric progression ratio that provides a constant rate of return over the time period. CAGR is not an accounting
Lexis diagram
In demography a Lexis diagram (named after economist and social scientist Wilhelm Lexis) is a two dimensional diagram used to represent events (such as births or deaths) that occur to individuals belo
Enrolled actuary
An enrolled actuary is an actuary enrolled by the Joint Board for the Enrollment of Actuaries under the Employee Retirement Income Security Act of 1974 (ERISA). Enrolled actuaries, under regulations o
Underwriting (UW) services are provided by some large financial institutions, such as banks, insurance companies and investment houses, whereby they guarantee payment in case of damage or financial lo
Esscher principle
The Esscher principle is an . It is given by , where is a strictly positive parameter. This premium is the for a risk , where denotes the moment generating function. The Esscher principle is a risk me
Risk inclination model
Risk inclination (RI) is defined as a mental disposition (i.e., confidence) toward an eventuality (i.e., a predicted state) that has consequences (i.e., either loss or gain). The risk inclination mode
Maximum life span
Maximum life span (or, for humans, maximum reported age at death) is a measure of the maximum amount of time one or more members of a population have been observed to survive between birth and death.
Extreme value theory
Extreme value theory or extreme value analysis (EVA) is a branch of statistics dealing with the extreme deviations from the median of probability distributions. It seeks to assess, from a given ordere
Truncated regression model
Truncated regression models are a class of models in which the sample has been truncated for certain ranges of the dependent variable. That means observations with values in the dependent variable bel
Economic capital
In finance, mainly for financial services firms, economic capital (ecap) is the amount of risk capital, assessed on a realistic basis, which a firm requires to cover the risks that it is running or co
Confidence weighting
Confidence weighting (CW) is concerned with measuring two variables: (1) what a respondent believes is a correct answer to a question and (2) what degree of certainty the respondent has toward the cor
Credit risk
A credit risk is risk of default on a debt that may arise from a borrower failing to make required payments. In the first resort, the risk is that of the lender and includes lost principal and interes
Years of potential life lost
Years of potential life lost (YPLL) or potential years of life lost (PYLL), is an estimate of the average years a person would have lived if they had not died prematurely. It is, therefore, a measure
Credibility theory
Credibility theory is a form of statistical inference used to forecast an uncertain future event developed by Thomas Bayes. It is employed to combine multiple estimates into a summary estimate that ta
Ruin theory
In actuarial science and applied probability, ruin theory (sometimes risk theory or collective risk theory) uses mathematical models to describe an insurer's vulnerability to insolvency/ruin. In such
Loss reserving
Loss reserving refers to the calculation of the required reserves for a tranche of general insurance business. It includes outstanding claims reserves. Typically, the claims reserves represent the mon
Failure rate
Failure rate is the frequency with which an engineered system or component fails, expressed in failures per unit of time. It is usually denoted by the Greek letter λ (lambda) and is often used in reli
A disease is a particular abnormal condition that negatively affects the structure or function of all or part of an organism, and that is not immediately due to any external injury. Diseases are often
Private Market Assets
Private market assets refer to investments in equity (shares) and debt issued by privately owned (non listed) companies – as opposed to ‘public’ (listed) corporations. These markets include private eq
Stock sampling
Stock sampling is sampling people in a certain state at the time of the survey. This is in contrast to flow sampling, where the relationship of interest deals with duration or survival analysis. In st
Vector generalized linear model
In statistics, the class of vector generalized linear models (VGLMs) was proposed to enlarge the scope of models catered for by generalized linear models (GLMs).In particular, VGLMs allow for response
Gompertz–Makeham law of mortality
The Gompertz–Makeham law states that the human death rate is the sum of an age-dependent component (the Gompertz function, named after Benjamin Gompertz), which increases exponentially with age and an
Financial economics
Financial economics, also known as finance, is the branch of economics characterized by a "concentration on monetary activities", in which "money of one type or another is likely to appear on both sid
Actuarial notation
Actuarial notation is a shorthand method to allow actuaries to record mathematical formulas that deal with interest rates and life tables. Traditional notation uses a where symbols are placed as super
Annual growth rate
Annual growth rate (AGR) is the change in the value of a measurement over the period of a year.
CRESTA (Catastrophe Risk Evaluation and Standardizing Target Accumulations) was founded as a joint project of Swiss Reinsurance Company, Gerling-Konzern Globale Reinsurance Company, and Munich Reinsur
Actuarial credentialing and exams
The actuarial credentialing and exam process usually requires passing a rigorous series of professional examinations, most often taking several years in total, before one can become recognized as a cr
Age stratification
In sociology, age stratification refers to the hierarchical ranking of people into age groups within a society. Age stratification could also be defined as a system of inequalities linked to age. In W
Maximum Downside Exposure
In financial investment, the Maximum downside exposure (MDE) values the maximum downside to an investment portfolio. In other words, it states the most that the portfolio could lose in the event of a
Pareto distribution
The Pareto distribution, named after the Italian civil engineer, economist, and sociologist Vilfredo Pareto (Italian: [paˈreːto] US: /pəˈreɪtoʊ/ pə-RAY-toh), is a power-law probability distribution th
Workers' compensation
Workers' compensation or workers' comp is a form of insurance providing wage replacement and medical benefits to employees injured in the course of employment in exchange for mandatory relinquishment
Rate making
Rate making, or insurance pricing, is the determination of rates charged by insurance companies. The benefit of rate making is to ensure insurance companies are setting fair and adequate premiums give
Insurance cycle
Insurance Cycle is a term describing the tendency of the insurance industry to swing between profitable and unprofitable periods over time is commonly known as the underwriting or insurance cycle.
Bornhuetter–Ferguson method
The Bornhuetter–Ferguson method is a loss reserving technique in insurance.
An actuary is a business professional who deals with the measurement and management of risk and uncertainty. The name of the corresponding field is actuarial science. These risks can affect both sides
Financial security system
A financial security system finances unknown future obligations. Such a system involves an arrangement between a provider, who agrees to pay the future obligations, often in return for payments from a
Financial modeling
Financial modeling is the task of building an abstract representation (a model) of a real world financial situation. This is a mathematical model designed to represent (a simplified version of) the pe
Ulpian's life table
Ulpian's life table is an ancient Roman annuities table. It is known through a passage, originating from the jurist Aemilius Macer, preserved in edited form in Justinian's Digest. The table appears to
Late-life mortality deceleration
In gerontology, late-life mortality deceleration is the disputed theory that hazard rate increases at a decreasing rate in late life rather than increasing exponentially as in the Gompertz law. Late-l
Actuarial science
Actuarial science is the discipline that applies mathematical and statistical methods to assess risk in insurance, pension, finance, investment and other industries and professions. More generally, ac
Value at risk
Value at risk (VaR) is a measure of the risk of loss for investments. It estimates how much a set of investments might lose (with a given probability), given normal market conditions, in a set time pe
Financial risk modeling
Financial risk modeling is the use of formal mathematical and econometric techniques to measure, monitor and control the market risk, credit risk, and operational risk on a firm's balance sheet, on a
Worker's compensation (Germany)
No description available.
Financial condition report
In accounting, a financial condition report (FCR) is a report on the solvency condition of an insurance company that takes into account both the current financial status, as reflected in the balance s
Auto insurance risk selection
Auto insurance risk selection is the process by which vehicle insurers determine whether or not to insure an individual and what insurance premium to charge. Depending on the jurisdiction, the insuran
(a,b,0) class of distributions
In probability theory, a member of the (a, b, 0) class of distributions is any distribution of a discrete random variable N whose values are nonnegative integers whose probability mass function satisf
IFRS 4 is an International Financial Reporting Standard (IFRS) issued by the International Accounting Standards Board (IASB) providing guidance for the accounting of insurance contracts. The standard
Future interests (actuarial science)
Future interests is the subset of actuarial math that divides enjoyment of property -- usually the right to an income stream either from an annuity, a trust, royalties, or rents -- based usually on th
Wilkie investment model
The Wilkie investment model, often just called Wilkie model, is a stochastic asset model developed by A. D. Wilkie that describes the behavior of various economics factors as stochastic time series. T
Enterprise risk management
Enterprise risk management (ERM) in business includes the methods and processes used by organizations to manage risks and seize opportunities related to the achievement of their objectives. ERM provid
Lee–Carter model
The Lee–Carter model is a numerical algorithm used in mortality forecasting and life expectancy forecasting. The input to the model is a matrix of age specific mortality rates ordered monotonically by
Ogden tables
Ogden tables are a set of statistical tables and other information for use in court cases in the UK. Their purpose is to make it easier to calculate future losses in personal injury and fatal accident
Reinsurance Actuarial Premium
Actuarial reinsurance premium calculation uses the similar mathematical tools as actuarial insurance premium. Nevertheless, Catastrophe modeling, Systematic risk or risk aggregation statistics tools a
Asset allocation
Asset allocation is the implementation of an investment strategy that attempts to balance risk versus reward by adjusting the percentage of each asset in an investment portfolio according to the inves
Reinsurance is insurance that an insurance company purchases from another insurance company to insulate itself (at least in part) from the risk of a major claims event. With reinsurance, the company p
Actuarial reserves
In insurance, an actuarial reserve is a reserve set aside for future insurance liabilities. It is generally equal to the actuarial present value of the future cash flows of a contingent event. In the
Replicating portfolio
In mathematical finance, a replicating portfolio for a given asset or series of cash flows is a portfolio of assets with the same properties (especially cash flows). This is meant in two distinct sens
Risk appetite
Risk appetite is the level of risk that an organization is prepared to accept in pursuit of its objectives, before action is deemed necessary to reduce the risk. It represents a balance between the po
Average high cost multiple
In unemployment insurance (UI) in the United States, the average high-cost multiple (AHCM) is a commonly used actuarial measure of Unemployment Trust Fund adequacy. Technically, AHCM is defined as res
Risk aversion
In economics and finance, risk aversion is the tendency of people to prefer outcomes with low uncertainty to those outcomes with high uncertainty, even if the average outcome of the latter is equal to
Area compatibility factor
In survival analysis, the area compatibility factor, F, is used in indirect standardisation of population mortality rates. where: is the standardised central exposed-to risk from age x to x + t for th
Theory of fructification
In economics, the theory of fructification is a theory of the interest rate which was proposed by French economist and finance minister Anne Robert Jacques Turgot. The term theory of fructification is
Heavy-tailed distribution
In probability theory, heavy-tailed distributions are probability distributions whose tails are not exponentially bounded: that is, they have heavier tails than the exponential distribution. In many a
Coherent risk measure
In the fields of actuarial science and financial economics there are a number of ways that risk can be defined; to clarify the concept theoreticians have described a number of properties that a risk m
Measuring attractiveness by a categorical-based evaluation technique (MACBETH)
Measuring attractiveness through a categorical-based evaluation technique (MACBETH) is a multiple-criteria decision analysis (MCDA) method that evaluates options against multiple criteria. MACBETH was
Copula (probability theory)
In probability theory and statistics, a copula is a multivariate cumulative distribution function for which the marginal probability distribution of each variable is uniform on the interval [0, 1]. Co
Incurred but not reported
In insurance, incurred but not reported (IBNR) claims is the amount owed by an insurer to all valid claimants who have had a covered loss but have not yet reported it. Since the insurer knows neither
Sampling risk
Sampling risk is one of the many types of risks an auditor may face when performing the necessary procedure of audit sampling. Audit sampling exists because of the impractical and costly effects of ex
Decrement table
Decrement tables, also called life table methods, are used to calculate the probability of certain events.
100-year flood
A 100-year flood is a flood event that has a 1 in 100 chance (1% probability) of being equaled or exceeded in any given year. The 100-year flood is also referred to as the 1% flood, since its annual e
Expected shortfall
Expected shortfall (ES) is a risk measure—a concept used in the field of financial risk measurement to evaluate the market risk or credit risk of a portfolio. The "expected shortfall at q% level" is t
Model risk
In finance, model risk is the risk of loss resulting from using insufficiently accurate models to make decisions, originally and frequently in the context of valuing financial securities. However, mod
Force of mortality
In actuarial science, force of mortality represents the instantaneous rate of mortality at a certain age measured on an annualized basis. It is identical in concept to failure rate, also called hazard
Embedded value
The Embedded Value (EV) of a life insurance company is the present value of future profits plus adjusted net asset value. It is a construct from the field of actuarial science which allows insurance c
Actuarial Society of South Africa HIV/AIDS models
The Actuarial Society of South Africa HIV/AIDS models, also known as ASSA AIDS models, are a series of mathematical models developed to assist the actuarial profession and the in assessing and address
John Graunt
John Graunt (24 April 1620 – 18 April 1674) has been regarded as the founder of demography. Graunt was one of the first demographers, and perhaps the first epidemiologist, though by profession he was
Vine copula
A vine is a graphical tool for labeling constraints in high-dimensional probability distributions. A regular vine is a special case for which all constraints are two-dimensional or conditional two-dim
Age at risk
Age at Risk (AaR) is a time-based risk measure designed to measure longevity risk in actuarial models. AaR represents certain quantile for a given probability distribution, so is similar to Value at R
Life table
In actuarial science and demography, a life table (also called a mortality table or actuarial table) is a table which shows, for each age, what the probability is that a person of that age will die be
German Statutory Accident Insurance
German Statutory Accident Insurance or workers' compensation is among the oldest branches of German social insurance. Occupational accident insurance was established in Germany by statute in 1884. It
Preventable years of life lost
Preventable years of life lost (PrYLL) is an epidemiological measure. It is an estimate of the average years a person would have lived if s/he had not died prematurely due to a preventable cause of de
Discounting is a financial mechanism in which a debtor obtains the right to delay payments to a creditor, for a defined period of time, in exchange for a charge or fee. Essentially, the party that owe
Solvency ratio
A solvency ratio measures the extent to which assets cover commitments for future payments, the liabilities. The solvency ratio of an insurance company is the size of its capital relative to all risks
Outline of actuarial science
The following outline is provided as an overview of and topical guide to actuarial science: Actuarial science – discipline that applies mathematical and statistical methods to assess risk in the insur
European embedded value
The European embedded value (EEV) is an effort by the CFO Forum to standardize the calculation of the embedded value. For this purpose the CFO Forum has released guidelines how embedded value should b
Wald's equation
In probability theory, Wald's equation, Wald's identity or Wald's lemma is an important identity that simplifies the calculation of the expected value of the sum of a random number of random quantitie
Risk inclination formula
The risk inclination formula uses the principle of moments, or Varignon's theorem, to calculate the first factorial moment of probability in order to define this center point of balance among all conf
Multi-attribute global inference of quality
Multi-attribute global inference of quality (MAGIQ) is a multi-criteria decision analysis technique. MAGIQ is based on a hierarchical decomposition of comparison attributes and rating assignment using
Hattendorff's theorem
Hattendorff's Theorem, attributed to (1868), is a theorem in actuarial science that describes the allocation of the variance or risk of the loss random variable over the lifetime of an actuarial reser
Compound interest
Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest. It is the result of reinvesting interest, or adding it
Actuarial control cycle
The actuarial control cycle is a specific business activity which involves the application of actuarial science to real world business problems. The actuarial control cycle requires a professional wit
Risk-adjusted return on capital
Risk-adjusted return on capital (RAROC) is a risk-based profitability measurement framework for analysing risk-adjusted financial performance and providing a consistent view of profitability across bu
Vienna Institute of Demography
The Vienna Institute of Demography (VID) (until 2002: Institut für Demographie/IfD) is a research institute of the division for humanities and social sciences within the Austrian Academy of Sciences (
Variance function
In statistics, the variance function is a smooth function which depicts the variance of a random quantity as a function of its mean. The variance function is a measure of heteroscedasticity and plays
Loss development factor
Loss development factors or LDFs are used in insurance pricing and reserving to adjust claims to their projected ultimate level. Insurance claims, especially in long-tailed lines such as liability ins
Kaplan–Meier estimator
The Kaplan–Meier estimator, also known as the product limit estimator, is a non-parametric statistic used to estimate the survival function from lifetime data. In medical research, it is often used to
Risk measure
In financial mathematics, a risk measure is used to determine the amount of an asset or set of assets (traditionally currency) to be kept in reserve. The purpose of this reserve is to make the risks t
Time value of money
The time value of money is the widely accepted conjecture that there is greater benefit to receiving a sum of money now rather than an identical sum later. It may be seen as an implication of the late
Regression analysis
In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships between a dependent variable (often called the 'outcome' or 'response' variable, or a 'l
Credit valuation adjustment
Credit valuation adjustments (CVAs) are accounting adjustments made to reserve a portion of profits on uncollateralized financial derivatives. They are charged by a bank to a risky (capable of default
Risk parity
Risk parity (or risk premia parity) is an approach to investment management which focuses on allocation of risk, usually defined as volatility, rather than allocation of capital. The risk parity appro
Stochastic modelling (insurance)
"Stochastic" means being or having a random variable. A stochastic model is a tool for estimating probability distributions of potential outcomes by allowing for random variation in one or more inputs
Risk management
Risk management is the identification, evaluation, and prioritization of risks (defined in ISO 31000 as the effect of uncertainty on objectives) followed by coordinated and economical application of r
Chain-ladder method
The chain-ladder or development method is a prominent actuarial loss reserving technique. The chain-ladder method is used in both the property and casualty and health insurance fields. Its intent is t
General insurance
General insurance or non-life insurance policy, including automobile and homeowners policies, provide payments depending on the loss from a particular financial event. General insurance is typically d
Cohort (statistics)
In statistics, marketing and demography, a cohort is a group of subjects who share a defining characteristic (typically subjects who experienced a common event in a selected time period, such as birth
Generalized linear model
In statistics, a generalized linear model (GLM) is a flexible generalization of ordinary linear regression. The GLM generalizes linear regression by allowing the linear model to be related to the resp
Asset/liability modeling
Asset/liability modeling is the process used to manage the business and financial objectives of a financial institution or an individual through an assessment of the portfolio assets and liabilities i
Gompertz distribution
In probability and statistics, the Gompertz distribution is a continuous probability distribution, named after Benjamin Gompertz. The Gompertz distribution is often applied to describe the distributio
Financial models with long-tailed distributions and volatility clustering
Financial models with long-tailed distributions and volatility clustering have been introduced to overcome problems with the realism of classical financial models. These classical models of financial
Mathematical statistics
Mathematical statistics is the application of probability theory, a branch of mathematics, to statistics, as opposed to techniques for collecting statistical data. Specific mathematical techniques whi
List of fictional actuaries
Fictional actuaries and the appearance of actuaries in works of fiction have been the subject of a number of articles in actuarial journals.
Defensive expenditures
In environmental accounting, defensive expenditures are expenditures that seek to minimise potential damage to oneself. Examples include defence and insurance.
Catastrophe modeling
Catastrophe modeling (also known as cat modeling) is the process of using computer-assisted calculations to estimate the losses that could be sustained due to a catastrophic event such as a hurricane
De Moivre's law
De Moivre's Law is a survival model applied in actuarial science, named for Abraham de Moivre. It is a simple law of mortality based on a linear survival function.
Risk intelligence
Risk intelligence is a concept that generally means "beyond risk management", though it has been used in different ways by different writers. The term is being used more frequently by business strateg
Esscher transform
In actuarial science, the Esscher transform is a transform that takes a probability density f(x) and transforms it to a new probability density f(x; h) with a parameter h. It was introduced by F. Essc
Mortality forecasting
Mortality forecasting refers to the art and science of determining likely future mortality rates. It is especially important in rich countries with a high proportion of aged people, since aged populat
Predictive analytics
Predictive analytics encompasses a variety of statistical techniques from data mining, predictive modeling, and machine learning that analyze current and historical facts to make predictions about fut
Mortality rate
Mortality rate, or death rate, is a measure of the number of deaths (in general, or due to a specific cause) in a particular population, scaled to the size of that population, per unit of time. Mortal
Insider investment strategy
The insider investment strategy is an investment strategy that follows the buying and selling decisions of so-called "insiders" in a stock market. The primary insiders have an advantage because they h
Insurance score
An insurance score – also called an insurance credit score – is a numerical point system based on select credit report characteristics. There is no direct relationship to financial credit scores used
Longevity risk
A longevity risk is any potential risk attached to the increasing life expectancy of pensioners and policy holders, which can eventually result in higher pay-out ratios than expected for many pension
Joint Board for the Enrollment of Actuaries
The Joint Board for the Enrollment of Actuaries licenses actuaries to perform a variety of actuarial tasks required of pension plans in the United States by the Employee Retirement Income Security Act
Pension fund investment in infrastructure
Although traditionally the preserve of governments and municipal authorities, infrastructure has recently become an asset class in its own right for private-sector investors, most notably pension fund
Experience modifier
In the insurance industry in the United States, an experience modifier or experience modification is an adjustment of an employer's premium for worker's compensation coverage based on the losses the i
The RiskMetrics variance model (also known as exponential smoother) was first established in 1989, when Sir Dennis Weatherstone, the new chairman of J.P. Morgan, asked for a daily report measuring and
Late-life mortality plateau
No description available.
Tail value at risk
Tail value at risk (TVaR), also known as tail conditional expectation (TCE) or conditional tail expectation (CTE), is a risk measure associated with the more general value at risk. It quantifies the e
Increased limit factor
Increased limit factors or ILFs are multiplicative factors that are applied to premiums for "basic" limits of coverage to determine premiums for higher limits of coverage. They are commonly used in ca
Demography (from Ancient Greek δῆμος (dêmos) 'people, society', and -γραφία (-graphía) 'writing, drawing, description') is the statistical study of populations, especially human beings. Demographic an