Actuarial acronyms and notation

Embarking on a career as a junior actuary within an insurance company is an exciting but challenging journey. Amidst the complexities of the field, one of your initial hurdles will be acquainting yourself with the multitude of acronyms that permeate actuarial discussions and documents.

In this comprehensive guide, we've diligently compiled an extensive list of these actuarial acronyms, making it easier for you to navigate the intricate world of insurance and risk assessment.

Actuarial acronyms

AcronymFull name
CSMContractual Service Margin
EEVEuropean Embedded Value
EIOPAEuropean Insurance and Occupational Pensions Authority
ESGEconomic Scenario Generator
EVEmbedded Value
FSFree Surplus
GMGeneral Model
IFRSInternational Financial Reporting Standard
IMInternal Model
MAMatching Adjustment
MCEVMarket-Consistent Embedded Value
NBNew Business
NSTNational Specific Template
ORSA Own Risk and Solvency Assessment
QRTQuantitative Reporting Template
RARisk Adjustment
RMRisk Margin
RSRRegular Supervisory Report
SCRSolvency Capital Requirement
SFStandard Formula
SFCRSolvency and Financial Condition Report
UFRUltimate Forward Rate
VAVolatility Adjustment
VFAVariable Fee Approach
VIFValue In-Force

Actuarial notation


\( i \) The effective rate of interest, namely, the total interest earned on 1 in a year on the assumption that the actual interest (if receivable otherwise than yearly) is invested forthwith as it becomes due on the same terms as the original principal.
\( v \) The present value of 1 due a year hence.
\( v = \frac{1}{1+i} \)
\( d \) The discount on i due a year hence.
\( d = 1 - v \)
\( \require{enclose} a_{\enclose{actuarial}{n}} \) The value of an annuity-certain of \( 1 \) per annum for \( n \) years, the payments being made at the end of each year.
\( \require{enclose} a_{\enclose{actuarial}{n}} = v + v^{2} + ... + v^{n} \)
\( \require{enclose} \ddot{a}_{\enclose{actuarial}{n}} \) The value of an annuity-certain of \( 1 \) per annum for \( n \) years, the payments being made at the beginning of each year.
\( \require{enclose} \ddot{a}_{\enclose{actuarial}{n}} = 1 + v + v^{2} + ... + v^{n-1} \)

Mortality tables

\( p_{x} \) The probability that (x) will live 1 year (survival).
\( q_{x} \) The probability that (x) will die within 1 year (mortality).
\( {}_{n} p_{x} \) The probability that (x) will live n years.
\( {}_{n} q_{x} \) The probability that (x) will die within n years.
\( a_{x} \) An annuity, first payment at the end of a year, to continue during the life of (x).
\( \ddot{a}_{x} \) An annuity-due to continue during the life of (x), the first payment to be made at once.
\( \ddot{a}_{x} = 1+a_{x} \)
\( \ddot{a}_{x} = \displaystyle\sum_{k=0}^{\infty} v^{k} \cdot {}_{k} p_{x} \)
\( \require{enclose} a^{}_{x:} {}^{}_{\enclose{actuarial}{n}} \) n-year temporary life annuity of (x)
\( {}_{m|} a_{x} \) m-year deferred whole life annuity of (x)
\( A_{x} \) whole life insurance of (x)
\( A_{x} = \displaystyle\sum_{k=0}^{\infty} v^{k+1} \cdot {}_{k} p_{x} \cdot q_{x+k} \)
\( \require{enclose} A^1_{x:} {}^{}_{\enclose{actuarial}{n}} \) n-year term insurance of (x)
\( \require{enclose} A^{}_{x:} {}^{1}_{\enclose{actuarial}{n}} \) n-year pure endowment of (x)
\( \require{enclose} A^{}_{x:} {}^{}_{\enclose{actuarial}{n}} \) n-year endowment insurance of (x)
\( {}_{m|} A_{x} \) m-year deferred insurance of (x)

If you come across any actuarial acronyms or notations that we've missed, or if you have any suggestions for enhancing this resource, please don't hesitate to reach out to us. We value your input and are committed to continually improving this reference guide to better assist aspiring actuaries like you. Best of luck in your actuarial journey!

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