LX* function

Actuarial Excel Addin

See the tutorial on Youtube

The LX* function, from the actuarial notation \(l_x\), returns a vector of 122 elements, from age \(x=0\) to age \(x=121\). Each element represents the number of lives surviving at age \(x\) from an initial cohort of lives at age = 0.

\[l_x = \begin{cases} 1,000,000, & \text{for } x = 0 \\ l_{x-1}\;p_{x-1}=l_{x-1}\;(1 - q_{x-1}), & \text{for } 0 < x \leq 121 \\ \end{cases}\]

The parameters of the LX* function determined which mortality table is used and what adjustments and projection, if any, must be made to the mortality rates (\(q_x\)).

The LX* function is never used alone, it is always a parameter of one of the following functions: JS, JL, LifeIns, TPX, TQX, GetLx, LifeExpectancy, CERTAIN.

* : Starting with version 4.5.3, LX can be called using LX or LX_aea.

** : Required parameter

Parameters
Default
Description
Sex**
--
\[\text{Sex} =\begin{cases}1&q_x^{Male}\\ \cdots&\cdots\\1.75\;&0.25\;q_x^{Male}+0.75\;q_x^{Female}\\ \cdots&\cdots\\2&q_x^{Female}\end{cases}\]
Qx table
UP94ICA
Mortality table, Canada and U.S.A.
Age move
0
\(q_x^{age\;move} = q_{x+age\;move}\), with the necessary adjustments at beginning and end of mortality table
Load
0
\(q_x^{load} = q_x\; (1 + load)\), respecting \(0\le q_x^{load}\le 1\)
Projection
False
True: With mortality projection
Projection scale
--
Projection scale, Canada and U.S.A. (must be set when 'Projection' is True)
Projection base year
--
Base year of the mortality table, e.g. 2014 for the CPM2014 (must be set when 'Projection' is True)
Year of valuation
--
..... (must be set when 'Projection' is True)
Age at valuation
--
..... (must be set to use 2D projection scale, 0 or empty otherwise)

A 1D projection scale contains the yearly mortality improvement rate for each mortality rate (i.e. one improvement rate for each age of the mortality table). The number of years of projection is equal to 'Year of valuation' minus 'Projection base year'.

A 2D projection scale contains the mortality improvement for each age of the mortality table and for each year (i.e. multiple improvement rates for each age of the mortality table).