Actuaries use a lot of acronyms, and keeping track of them all can be tricky. Whether you're new to the field or have years of experience, you've probably come across abbreviations that left you guessing.
This guide is here to help. It's a collection of actuarial acronyms, all in one place, so you can quickly find what they mean.
List of content:
Actuarial acronyms
| Acronym | Full name |
|---|---|
| CSM | Contractual Service Margin |
| EEV | European Embedded Value |
| EIOPA | European Insurance and Occupational Pensions Authority |
| ESG | Economic Scenario Generator |
| ESG | Environmental, Social and Governance |
| EV | Embedded Value |
| FS | Free Surplus |
| GM | General Model |
| IF | In-Force |
| IFRS | International Financial Reporting Standard |
| IM | Internal Model |
| MA | Matching Adjustment |
| MCEV | Market-Consistent Embedded Value |
| NB | New Business |
| NST | National Specific Template |
| ORSA | Own Risk and Solvency Assessment |
| P&L | Profit and Loss |
| QRT | Quantitative Reporting Template |
| RA | Risk Adjustment |
| RM | Risk Margin |
| RSR | Regular Supervisory Report |
| SCR | Solvency Capital Requirement |
| SF | Standard Formula |
| SFCR | Solvency and Financial Condition Report |
| UFR | Ultimate Forward Rate |
| UL | Unit-Linked |
| VA | Volatility Adjustment |
| VFA | Variable Fee Approach |
| VIF | Value In-Force |
| YE | Year End |
Actuarial notation
Interest
| Symbol | Meaning |
|---|---|
| \( i \) | 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. |
| \( i^{(m)} \) | The nominal rate of interest, convertible \( m \) times a year. |
| \( v \) | 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. \( \require{enclose} a_{\enclose{actuarial}{n}} = \sum_{k=1}^{n} v^k \) |
| \( \require{enclose} \ddot{a}_{\enclose{actuarial}{n}} \) | The value of an annuity-certain of \( 1 \) per annum for \( n \) years, the payments being made at the beginning of each year. \( \require{enclose} \ddot{a}_{\enclose{actuarial}{n}} = \sum_{k=0}^{n-1} v^k \) |
| \( \require{enclose} s_{\enclose{actuarial}{n}} \) | The accumulated value of an annuity-certain of \( 1 \) per annum for \( n \) years, with payments made at the end of each year. \( \require{enclose} s_{\enclose{actuarial}{n}} = \sum_{k=0}^{n-1} (1+i)^k \) |
| \( \require{enclose} \ddot{s}_{\enclose{actuarial}{n}} \) | The accumulated value of an annuity-certain of \( 1 \) per annum for \( n \) years, with payments made at the beginning of each year. \( \require{enclose} \ddot{s}_{\enclose{actuarial}{n}} = \sum_{k=1}^{n} (1+i)^k \) |
Mortality tables
| Symbol | Meaning |
|---|---|
| \( l_{x} \) | The number of persons who attain age \( x \) according to the mortality table. |
| \( l_{[x]+t} \) | The number in the select life table who were selected at age \( x \) and have attained age \( x+t \). |
| \( d_{x} \) |
The number of persons who die between ages \( x \) and \( x+t \) according to the mortality table. \( d_{x} = l_{x} - l_{x+1} \) |
| \( p_{x} \) | 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. |
| \( {}_{n|} q_{x} \) | The probability that \( (x) \) will die in a year, deferred \( n \) years; that is, that he will die in the \( (n + i)^{\text{th}} \) year. |
| \( {}_{n} {q}_{\overline{xy}} \) | The [robability that the survivor of the two lives \( (x) \) and \( (y) \) will die within \( n \) years |
| \( e_{x} \) | The curtate expectation of life (or average after-lifetime) of \( (x) \). |
| \( m_{x} \) | The central death-rate for the year of age \( x \) to \( x + 1 \). |
Life annuities
| Symbol | Meaning |
|---|---|
| \( a_{x} \) | 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 \( (x) \). |
| \( {}_{n|} a_{x} \) | n-year deferred whole life annuity of \( (x) \). |
| \( {}_{n|t} a_{x} \) | A deferred temporary annuity on \( (x) \) deferred \( n \) years and, after that, to run for \( t \) years. |
| \( a_{x}^{(m)} \) | An annuity on \( (x) \) payable by \( m \) instalments of \( \frac{1}{m} \) each throughout the year, the first payment being one of \( \frac{1}{m} \) at the end of the first 1/m-th of a year. |
| \( a_{xyz} \) | An annuity, first payment at the end of a year, to continue during the joint lives of \( (x) \), \( (y) \) and \( (z) \). |
| \( a_{y|x} \) | A reversionary annuity, that is, an annuity on the life of \( (x) \) after the death of \( (y) \). |
| \( a_{\overline{xyz}} \) | An annuity payable so long as at least one of the three lives \( (x) \), \( (y) \) and \( (z) \) is alive. |
| \( Ia \) | An annuity increasing 1 per annum. |
| \( a_{[x]} \) | Value of an annuity on a life now aged \( x \) and now select. |
| \( a_{[x-n]+n} \) | value of an annuity on a life now aged \( x \) and select \( n \) years ago at age \( x - n \). |
| \( s_{x} \) | The accumulated value of an annuity, with the first payment at the end of a year, to continue during the life of \( (x) \). |
| \( \ddot{s}_{x} \) | The accumulated value of an annuity-due to continue during the life of \( (x) \), the first payment made at once. |
| \( \require{enclose} s^{}_{x:} {}^{}_{\enclose{actuarial}{n}} \) | The accumulated value of an n-year temporary life annuity of \( (x) \). |
| \( {}_{m|} s_{x} \) | The accumulated value of an m-year deferred whole life annuity of \( (x) \). |
Life insurance
| Symbol | Meaning |
|---|---|
| \( A_{x} \) | 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 \( (x) \) |
|
\( \require{enclose} A^{}_{x:} {}^{1}_{\enclose{actuarial}{n}} \) \( {}_{n} E_{x} \) |
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 \( (x) \) |
| \( A_{x}^{(m)} \) | An assurance payable at the end of that fraction \( \frac{1}{m} \) of a year in which \( (x) \) dies. |
| \( A_{xyz} \) | An assurance payable at the end of the year of the failure of the joint lives \( (x) \), \( (y) \) and \( (z) \). |
| \( A_{z|xy} \) | An assurance payable on the failure of the joint lives \( (x) \) and \( (y) \) provided both these lives survive \( (z) \). |
| \( {}_{n} A_{\overline{xy}} \) | An assurance payable at the end of the year of death of the survivor of the lives \( (x) \) and \( (y) \) provided the death occurs within \( n \) years. |
| \( P_{x} \) | The annual premium for an assurance payable at the end of the year of death of \( (x) \). |
| \( {}_{t} {V}_{x} \) | The value of an ordinary whole-llfe assurance on \( (x) \) which has been \( t \) years in force, the premium then just due being unpaid. |
| \( {}_{t} {W}_{x} \) | The paid-up policy the present value of which is \( {}_{t} {V}_{x} \). |
Commutation functions
| Symbol | Meaning |
|---|---|
| \( D_{x} \) |
Present value of a life aged \( (x) \) \( v^{x} \cdot l_{x}\) |
| \( N_{x} \) | \( D_{x} + D_{x+1} + D_{x+2} + ... \) |
| \( S_{x} \) | \( N_{x} + N_{x+1} + N_{x+2} + ... \) |
| \( C_{x} \) | \( v^{x+1} \cdot d_{x} \) |
| \( M_{x} \) | \( C_{x} + C_{x+1} + C_{x+2} + ... \) |
| \( R_{x} \) | \( M_{x} + M_{x+1} + M_{x+2} + ... \) |
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!