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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. Example notation using the halo system can be seen below.
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 ...
5.2 Investments & Asset Management. 5.3 Mathematics of Finance. 5.4 Mortality. 5.5 Pensions. 5.6 Other. ... Actuarial notation; Fields in which actuarial science is ...
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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%.
De Moivre's law first appeared in his 1725 Annuities upon Lives, the earliest known example of an actuarial textbook. [6] Despite the name now given to it, de Moivre himself did not consider his law (he called it a "hypothesis") to be a true description of the pattern of human mortality.
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 ...
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.