Source code for solvency2.model.LifeTable

"""Commutation functions and actuarial notations

The ``LifeTable`` space includes Cells to calculate
commutation functions and actuarial notations for given
``Sex``, ``IntRate`` and ``MortalityTable``. ``MortalityTable`` and
``Sex`` are used in :py:func:`qx` below to identify
the mortality rates to be applied.

Example:

    An example of ``LifeTable`` in the :mod:`simplelife` model::

        >>> space = simplelife.LifeTable

        >>> space.Sex = 'M'

        >>> space.IntRate = 0.03

        >>> space.MortalityTable = lambda sex, x: 0.001 if x < 110 else 1

        >>> space.AnnDuenx(40, 10)

References:
    * `International actuarial notation by F.S.Perryman <https://www.casact.org/pubs/proceed/proceed49/49123.pdf>`_
    * `Actuarial notations on Wikipedia <https://en.wikipedia.org/wiki/Actuarial_notation>`_

.. rubric:: Project Templates

This module is included in the following project templates.

* :mod:`simplelife`
* :mod:`nestedlife`

.. rubric:: References in Sub

Attributes:
    Sex: 'M' or 'F' to indicate male or female column in the mortality table.
    IntRate: The constant interest rate for discounting.
    MortalityTable: The ultimate mortality table by sex and age.

"""

from modelx.serialize.jsonvalues import *

_formula = lambda Sex, IntRate, TableID: None

_bases = []

_allow_none = None

_spaces = []

# ---------------------------------------------------------------------------
# Cells

[docs] def AnnDuenx(x, n, k=1, f=0): """ The present value of an annuity-due. .. math:: \\require{enclose}{}_{f|}\\ddot{a}_{x:\\enclose{actuarial}{n}}^{(k)} Args: x(int): age n(int): length of annuity payments in years k(int, optional): number of split payments in a year f(int, optional): waiting period in years """ if Dx(x) == 0: return 0 result = (Nx(x+f) - Nx(x+f+n)) / Dx(x) if k > 1: return result - (k-1) / (2*k) * (1 - Dx(x+f+n) / Dx(x)) else: return result
[docs] def AnnDuex(x, k, f=0): """The present value of a lifetime annuity due. Args: x(int): age k(int, optional): number of split payments in a year f(int, optional): waiting period in years """ if Dx(x) == 0: return 0 result = (Nx(x+f)) / Dx(x) if k > 1: return result - (k-1) / (2*k) else: return result
[docs] def Ax(x, f=0): """The present value of a lifetime assurance on a person at age ``x`` payable immediately upon death, optionally with an waiting period of ``f`` years. .. math:: \\require{enclose}{}_{f|}\\overline{A}_{x} """ if Dx(x) == 0: return 0 else: return Mx(x+f) / Dx(x)
[docs] def Axn(x, n, f=0): """The present value of an assurance on a person at age ``x`` payable immediately upon death, optionally with an waiting period of ``f`` years. .. math:: \\require{enclose}{}_{f|}\\overline{A}^{1}_{x:\\enclose{actuarial}{n}} """ if Dx(x) == 0: return 0 else: return (Mx(x+f) - Mx(x+f+n)) / Dx(x)
[docs] def Cx(x): """The commutation column :math:`\\overline{C_x}`. """ return dx(x) * disc()**(x+1/2)
[docs] def Dx(x): """The commutation column :math:`D_{x} = l_{x}v^{x}`. """ return lx(x) * disc() ** x
[docs] def Exn(x, n): """ The value of an endowment on a person at age ``x`` payable after n years .. math:: {}_{n}E_x """ if Dx(x) == 0: return 0 else: return Dx(x+n) / Dx(x)
[docs] def Mx(x): """The commutation column :math:`M_x`.""" if x >= 110: return Dx(x) else: return Mx(x+1) + Cx(x)
[docs] def Nx(x): """The commutation column :math:`N_x`.""" if x >= 110: # TODO: Get the last age from the table return Dx(x) else: return Nx(x+1) + Dx(x)
[docs] def disc(): """The discount factor :math:`v = 1/(1 + i)`.""" return 1 / (1 + IntRate)
[docs] def dx(x): """The number of persons who die between ages ``x`` and ``x+1``""" return lx(x) * qx(x)
[docs] def lx(x): """The number of persons remaining at age ``x``. """ if x == 0: return 100000 else: return lx(x-1) - dx(x-1)
[docs] def qx(x): """Probability that a person at age ``x`` will die in one year.""" return MortalityTable[TableID, Sex, x]
# --------------------------------------------------------------------------- # References Sex = "M" IntRate = 0.01 TableID = 1 MortalityTable = ("Pickle", 2325095460104)