International actuarial notation for life contingencies, annuities, and premiums.

Life Table Notation

$l_x$ : Number of lives at age $x$ in the life table
$d_x$ : Number of deaths between ages $x$ and $x+1$ ; $d_x = l_x - l_{x+1}$
$q_x$ : Probability of death within one year for a life aged $x$ ; $q_x = d_x / l_x$
$p_x$ : Probability of surviving one year; $p_x = 1 - q_x = l_{x+1} / l_x$
${}_{t}p_x$ : Probability of surviving $t$ years; ${}_{t}p_x = l_{x+t} / l_x$
${}_{t}q_x$ : Probability of dying within $t$ years; ${}_{t}q_x = 1 - {}_{t}p_x$
${}_{t|u}q_x$ : Probability of dying between times $t$ and $t+u$ ; $= {}_{t}p_x \cdot {}_{u}q_{x+t}$
$\mu_x$ : Force of mortality at age $x$

Insurance Notation

$A_x$ : APV of whole life insurance (discrete, paid at end of year of death)
$\bar{A}_x$ : APV of whole life insurance (continuous, paid at moment of death)
$A^1_{x:\overline{n}|}$ : APV of $n$ -year term life insurance
$A_{x:\overline{n}|}$ : APV of $n$ -year endowment insurance
${}^2A_x$ : Second moment of PV of whole life insurance (use $\delta' = 2\delta$ )

$\ddot{a}_x$ : APV of whole life annuity-due (payments at beginning of year)
$a_x$ : APV of whole life annuity-immediate (payments at end of year)
$\bar{a}_x$ : APV of continuous whole life annuity
$\ddot{a}_{x:\overline{n}|}$ : APV of $n$ -year temporary life annuity-due
${}_{n|}\ddot{a}_x$ : APV of $n$ -year deferred whole life annuity-due

$P_x$ : Net annual premium for whole life insurance
$P_{x:\overline{n}|}$ : Net annual premium for $n$ -year endowment
${}_{t}V_x$ : Net premium reserve at time $t$ for whole life insurance
${}_{t}V_{x:\overline{n}|}$ : Net premium reserve at time $t$ for $n$ -year endowment