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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.
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 .
As an example, consider a whole life insurance policy of one dollar issued on (x) with yearly premiums paid at the start of the year and death benefit paid at the end of the year. In actuarial notation, a benefit reserve is denoted as V. Our objective is to find the value of the net level premium reserve at time t.
In actuarial notation (x) denotes a status or life that has survived to age x, and T(x) is the future lifetime of (x) (T(x) is a random variable).
Hattendorff's Theorem, attributed to K. Hattendorff (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 reserve. In other words, Hattendorff's theorem demonstrates that the variation in the present value of the loss of an issued insurance ...
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. [1]
In actuarial notation, the probability of surviving from age to age + is denoted and the probability of dying during age (i.e. between ages and +) is denoted . For example, if 10% of a group of people alive at their 90th birthday die before their 91st birthday, the age-specific death probability at 90 would be 10%.
In mathematics, the Schuette–Nesbitt formula is a generalization of the inclusion–exclusion principle.It is named after Donald R. Schuette and Cecil J. Nesbitt.. The probabilistic version of the Schuette–Nesbitt formula has practical applications in actuarial science, where it is used to calculate the net single premium for life annuities and life insurances based on the general ...