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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 typically calculated for the benefit-payment or series of payments associated with life insurance and life annuities. The probability of a future payment is based on assumptions about the person's future mortality which is typically estimated using a life table. Life insurance Whole life insurance pays a pre-determined benefit either at or soon after the insured's death. The symbol ''(x)'' is used to denote "a life aged ''x''" where ''x'' is a non-random parameter that is assumed to be greater than zero. The actuarial present value of one unit of whole life insurance issued to ''(x)'' is denoted by the symbol \,A_x or \,\overline_x in actuarial notation. Let ''G>0'' (the "age at death") be the random variable that models the age at which an individual, such as ''(x)'', will die. And le ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Expected Value
In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first Moment (mathematics), moment) is a generalization of the weighted average. Informally, the expected value is the arithmetic mean, mean of the possible values a random variable can take, weighted by the probability of those outcomes. Since it is obtained through arithmetic, the expected value sometimes may not even be included in the sample data set; it is not the value you would expect to get in reality. The expected value of a random variable with a finite number of outcomes is a weighted average of all possible outcomes. In the case of a continuum of possible outcomes, the expectation is defined by Integral, integration. In the axiomatic foundation for probability provided by measure theory, the expectation is given by Lebesgue integration. The expected value of a random variable is often denoted by , , or , with a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Endowment Policy
An endowment policy is a life insurance contract designed to pay a lump sum after a specific term (on its 'maturity') or on death Death is the end of life; the irreversible cessation of all biological functions that sustain a living organism. Death eventually and inevitably occurs in all organisms. The remains of a former organism normally begin to decompose sh .... These are long-term policies, often designed to repay a mortgage loan, with typical maturities between ten and thirty years within certain age limits. Some policies also insure additional risks, such as critical illness. Policies are either traditional with-profits or unit-linked (including unitised with-profits funds). With both types of policy, the value varies with the underlying investments, but the mechanism by which growth is allocated varies. The sum insured remains payable on death or other insured events. Traditional with profits endowments There is an amount guaranteed to be paid out cal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Present Value
In economics and finance, present value (PV), also known as present discounted value (PDV), is the value of an expected income stream determined as of the date of valuation. The present value is usually less than the future value because money has interest-earning potential, a characteristic referred to as the time value of money, except during times of negative interest rates, when the present value will be equal or more than the future value. Time value can be described with the simplified phrase, "A dollar today is worth more than a dollar tomorrow". Here, 'worth more' means that its value is greater than tomorrow. A dollar today is worth more than a dollar tomorrow because the dollar can be invested and earn a day's worth of interest, making the total accumulate to a value more than a dollar by tomorrow. Interest can be compared to Renting, rent. Just as rent is paid to a landlord by a tenant without the ownership of the asset being transferred, interest is paid to a lender by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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, the probability that a person of that age will die before their next birthday ("probability of death"). In other words, it represents the survivorship of people from a certain population. They can also be explained as a long-term mathematical way to measure a population's longevity. Tables have been created by demographers including John Graunt, Reed and Merrell, Keyfitz, and Greville. There are two types of life tables used in actuarial science. The period life table represents mortality rates during a specific time period for a certain population. A cohort life table, often referred to as a generation life table, is used to represent the overall mortality rates of a certain population's entire lifetime. They must have had to be born during the same specific time interval. A cohort life table is more frequently used because it is able to m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Actuary
An actuary is a professional with advanced mathematical skills who deals with the measurement and management of risk and uncertainty. These risks can affect both sides of the balance sheet and require investment management, asset management, liability (financial accounting), liability management, and valuation skills. Actuaries provide assessments of financial security systems, with a focus on their complexity, their mathematics, and their mechanisms. The name of the corresponding academic discipline is actuarial science. While the concept of insurance dates to antiquity, the concepts needed to scientifically measure and mitigate risks have their origins in 17th-century studies of probability and annuities. Actuaries in the 21st century require analytical skills, business knowledge, and an understanding of human behavior and information systems; actuaries use this knowledge to design programs that manage risk, by determining if the implementation of strategies proposed for mit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 insurance context an actuarial reserve is the present value of the future cash flows of an insurance policy and the total liability of the insurer is the sum of the actuarial reserves for every individual policy. Regulated insurers are required to keep offsetting assets to pay off this future liability. The loss random variable The loss random variable is the starting point in the determination of any type of actuarial reserve calculation. Define K(x) to be the future state lifetime random variable of a person aged x. Then, for a death benefit of one dollar and premium P, the loss random variable, L, can be written in actuarial notation as a function of K(x) : L = v^ - P\ddot_ From this we can see that the present value of the loss to the insurance company now if the person dies i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 halo system, where symbols are placed as superscript or subscript before or after the main letter. Example notation using the halo system can be seen to the right. Various proposals have been made to adopt a linear system, where all the notation would be on a single line without the use of superscripts or subscripts. Such a method would be useful for computing where representation of the halo system can be extremely difficult. However, a standard linear system has yet to emerge. Example notation Interest rates \,i is the annual effective interest rate, which is the "true" rate of interest over ''a year''. Thus if the annual interest rate is 12% then \,i = 0.12. \,i^ (pronounced "i ''upper'' m") is the nominal interest rate convertible m times a year, and is numerically equal to m times the effective rate of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Actuarial Science
Actuarial science is the discipline that applies mathematics, mathematical and statistics, statistical methods to Risk assessment, assess risk in insurance, pension, finance, investment and other industries and professions. Actuary, Actuaries are professionals trained in this discipline. In many countries, actuaries must demonstrate their competence by passing a series of rigorous professional examinations focused in fields such as probability and predictive analysis. Actuarial science includes a number of interrelated subjects, including mathematics, probability theory, statistics, finance, economics, financial accounting and computer science. Historically, actuarial science used deterministic models in the construction of tables and premiums. The science has gone through revolutionary changes since the 1980s due to the proliferation of high speed computers and the union of stochastic actuarial models with modern financial theory. Many universities have undergraduate and gradu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Internal Rate Of Return
Internal rate of return (IRR) is a method of calculating an investment's rate of return. The term ''internal'' refers to the fact that the calculation excludes external factors, such as the risk-free rate, inflation, the cost of capital, or financial risk. The method may be applied either ex-post or ex-ante. Applied ex-ante, the IRR is an estimate of a future annual rate of return. Applied ex-post, it measures the actual achieved investment return of a historical investment. It is also called the discounted cash flow rate of return (DCFROR)Project Economics and Decision Analysis, Volume I: Deterministic Models, M.A.Main, Page 269 or yield rate. Definition (IRR) The IRR of an investment or project is the "annualized effective compounded return rate" or rate of return that sets the net present value (NPV) of all cash flows (both positive and negative) from the investment equal to zero. Equivalently, it is the interest rate at which the net present value of the future cash fl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Cumulative Distribution Function
In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable X, or just distribution function of X, evaluated at x, is the probability that X will take a value less than or equal to x. Every probability distribution Support (measure theory), supported on the real numbers, discrete or "mixed" as well as Continuous variable, continuous, is uniquely identified by a right-continuous Monotonic function, monotone increasing function (a càdlàg function) F \colon \mathbb R \rightarrow [0,1] satisfying \lim_F(x)=0 and \lim_F(x)=1. In the case of a scalar continuous distribution, it gives the area under the probability density function from negative infinity to x. Cumulative distribution functions are also used to specify the distribution of multivariate random variables. Definition The cumulative distribution function of a real-valued random variable X is the function given by where the right-hand side represents the probability ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Geometric Distribution
In probability theory and statistics, the geometric distribution is either one of two discrete probability distributions: * The probability distribution of the number X of Bernoulli trials needed to get one success, supported on \mathbb = \; * The probability distribution of the number Y=X-1 of failures before the first success, supported on \mathbb_0 = \ . These two different geometric distributions should not be confused with each other. Often, the name ''shifted'' geometric distribution is adopted for the former one (distribution of X); however, to avoid ambiguity, it is considered wise to indicate which is intended, by mentioning the support explicitly. The geometric distribution gives the probability that the first occurrence of success requires k independent trials, each with success probability p. If the probability of success on each trial is p, then the probability that the k-th trial is the first success is :\Pr(X = k) = (1-p)^p for k=1,2,3,4,\dots The above form of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 function, in reliability theory. Motivation and definition In a life table, we consider the probability of a person dying from age ''x'' to ''x'' + 1, called ''q''''x''. In the continuous case, we could also consider the conditional probability of a person who has attained age (''x'') dying between ages ''x'' and ''x'' + ''Δx'', which is :P_(\Delta x)=P(x |
