"""The main Space in the :mod:`~basiclife.BasicTerm_M` model.
:mod:`~basiclife.BasicTerm_M.Projection` is the only Space defined
in the :mod:`~basiclife.BasicTerm_M` model, and it contains
all the logic and data used in the model.
.. rubric:: Parameters and References
(In all the sample code below,
the global variable ``Projection`` refers to the
:mod:`~basiclife.BasicTerm_M.Projection` Space.)
Attributes:
model_point_table: All model point data as a DataFrame.
The sample model point data was generated by
*generate_model_points.ipynb* included in the library.
By default, :func:`model_point` returns this :attr:`model_point_table`.
The DataFrame has columns labeled ``age_at_entry``,
``sex``, ``policy_term``, ``policy_count``
and ``sum_assured``.
Cells defined in :mod:`~basiclife.BasicTerm_M.Projection`
with the same names as these columns return
the corresponding columns.
(``policy_count`` is not used by default.)
.. code-block::
>>> Projection.model_poit_table
age_at_entry sex policy_term policy_count sum_assured
point_id
1 47 M 10 1 622000
2 29 M 20 1 752000
3 51 F 10 1 799000
4 32 F 20 1 422000
5 28 M 15 1 605000
... .. ... ... ...
9996 47 M 20 1 827000
9997 30 M 15 1 826000
9998 45 F 20 1 783000
9999 39 M 20 1 302000
10000 22 F 15 1 576000
[10000 rows x 5 columns]
The DataFrame is saved in the Excel file *model_point_table.xlsx*
placed in the model folder.
:attr:`model_point_table` is created by
Projection's `new_pandas`_ method,
so that the DataFrame is saved in the separate file.
The DataFrame has the injected attribute
of ``_mx_dataclident``::
>>> Projection.model_point_table._mx_dataclient
<PandasData path='model_point_table.xlsx' filetype='excel'>
.. seealso::
* :func:`model_point`
* :func:`age_at_entry`
* :func:`sex`
* :func:`policy_term`
* :func:`sum_assured`
disc_rate_ann: Annual discount rates by duration as a pandas Series.
.. code-block::
>>> Projection.disc_rate_ann
year
0 0.00000
1 0.00555
2 0.00684
3 0.00788
4 0.00866
146 0.03025
147 0.03033
148 0.03041
149 0.03049
150 0.03056
Name: disc_rate_ann, Length: 151, dtype: float64
The Series is saved in the Excel file *disc_rate_ann.xlsx*
placed in the model folder.
:attr:`disc_rate_ann` is created by
Projection's `new_pandas`_ method,
so that the Series is saved in the separate file.
The Series has the injected attribute
of ``_mx_dataclident``::
>>> Projection.disc_rate_ann._mx_dataclient
<PandasData path='disc_rate_ann.xlsx' filetype='excel'>
.. seealso::
* :func:`disc_rate_mth`
* :func:`disc_factors`
mort_table: Mortality table by age and duration as a DataFrame.
See *basic_term_sample.xlsx* included in this library
for how the sample mortality rates are created.
.. code-block::
>>> Projection.mort_table
0 1 2 3 4 5
Age
18 0.000231 0.000254 0.000280 0.000308 0.000338 0.000372
19 0.000235 0.000259 0.000285 0.000313 0.000345 0.000379
20 0.000240 0.000264 0.000290 0.000319 0.000351 0.000386
21 0.000245 0.000269 0.000296 0.000326 0.000359 0.000394
22 0.000250 0.000275 0.000303 0.000333 0.000367 0.000403
.. ... ... ... ... ... ...
116 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000
117 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000
118 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000
119 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000
120 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000
[103 rows x 6 columns]
The DataFrame is saved in the Excel file *mort_table.xlsx*
placed in the model folder.
:attr:`mort_table` is created by
Projection's `new_pandas`_ method,
so that the DataFrame is saved in the separate file.
The DataFrame has the injected attribute
of ``_mx_dataclident``::
>>> Projection.mort_table._mx_dataclient
<PandasData path='mort_table.xlsx' filetype='excel'>
.. seealso::
* :func:`mort_rate`
* :func:`mort_rate_mth`
np: The `numpy`_ module.
pd: The `pandas`_ module.
.. _numpy:
https://numpy.org/
.. _pandas:
https://pandas.pydata.org/
.. _new_pandas:
https://docs.modelx.io/en/latest/reference/space/generated/modelx.core.space.UserSpace.new_pandas.html
"""
from modelx.serialize.jsonvalues import *
_formula = None
_bases = []
_allow_none = None
_spaces = []
# ---------------------------------------------------------------------------
# Cells
[docs]def age(t):
"""The attained age at time t.
Defined as::
age_at_entry() + duration(t)
.. seealso::
* :func:`age_at_entry`
* :func:`duration`
"""
return age_at_entry() + duration(t)
[docs]def age_at_entry():
"""The age at entry of the model points
The ``age_at_entry`` column of the DataFrame returned by
:func:`model_point`.
"""
return model_point()["age_at_entry"]
[docs]def claim_pp(t):
"""Claim per policy
The claim amount per plicy. Defaults to :func:`sum_assured`.
"""
return sum_assured()
[docs]def claims(t):
"""Claims
Claims during the period from ``t`` to ``t+1`` defined as::
claim_pp(t) * pols_death(t)
.. seealso::
* :func:`claim_pp`
* :func:`pols_death`
"""
return claim_pp(t) * pols_death(t)
[docs]def commissions(t):
"""Commissions
By default, 100% premiums for the first year, 0 otherwise.
.. seealso::
* :func:`premiums`
* :func:`duration`
"""
return (duration(t) == 0) * premiums(t)
[docs]def disc_factors():
"""Discount factors.
Vector of the discount factors as a Numpy array. Used for calculating
the present values of cashflows.
.. seealso::
:func:`disc_rate_mth`
"""
return np.array(list((1 + disc_rate_mth()[t])**(-t) for t in range(max_proj_len())))
[docs]def disc_rate_mth():
"""Monthly discount rate
Nummpy array of monthly discount rates from time 0 to :func:`max_proj_len` - 1
defined as::
(1 + disc_rate_ann)**(1/12) - 1
.. seealso::
:func:`disc_rate_ann`
"""
return np.array(list((1 + disc_rate_ann[t//12])**(1/12) - 1 for t in range(max_proj_len())))
[docs]def duration(t):
"""Duration in force in years"""
return t//12
[docs]def expense_acq():
"""Acquisition expense per policy
``300`` by default.
"""
return 300
[docs]def expense_maint():
"""Annual maintenance expense per policy
``60`` by default.
"""
return 60
[docs]def expenses(t):
"""Acquisition and maintenance expenses
Expense cashflow during the period from ``t`` to ``t+1``.
For any ``t``, the maintenance expense is recognized,
which is defined as::
pols_if(t) * expense_maint()/12 * inflation_factor(t)
At ``t=0`` only, the acquisition expense,
defined as :func:`expense_acq`, is recognized.
.. seealso::
* :func:`pols_if`
* :func:`expense_maint`
* :func:`inflation_factor`
.. versionchanged:: 0.2.0
The maintenance expense is also recognized for ``t=0``.
"""
return (t == 0) * expense_acq() * pols_if(t) \
+ pols_if(t) * expense_maint()/12 * inflation_factor(t)
[docs]def inflation_factor(t):
"""The inflation factor at time t
.. seealso::
* :func:`inflation_rate`
"""
return (1 + inflation_rate())**(t//12)
[docs]def inflation_rate():
"""Inflation rate"""
return 0.01
[docs]def lapse_rate(t):
"""Lapse rate
By default, the lapse rate assumption is defined by duration as::
max(0.1 - 0.02 * duration(t), 0.02)
.. seealso::
:func:`duration`
"""
return np.maximum(0.1 - 0.02 * duration(t), 0.02)
[docs]def loading_prem():
"""Loading per premium
``0.5`` by default.
.. seealso::
* :func:`premium_pp`
"""
return 0.5
max_proj_len = lambda: max(proj_len())
"""The max of all projection lengths
Defined as ``max(proj_len())``
.. seealso::
:func:`proj_len`
"""
[docs]def model_point():
"""Target model points
Returns as a DataFrame the model points to be in the scope of calculation.
By default, this Cells returns the entire :attr:`model_point_table`
without change.
To select model points, change this formula so that this
Cells returns a DataFrame that contains only the selected model points.
Examples:
To select only the model point 1::
def model_point():
return model_point_table.loc[1:1]
To select model points whose ages at entry are 40 or greater::
def model_point():
return model_point_table[model_point_table["age_at_entry"] >= 40]
Note that the shape of the returned DataFrame must be the
same as the original DataFrame, i.e. :attr:`model_point_table`.
When selecting only one model point, make sure the
returned object is a DataFrame, not a Series, as seen in the example
above where ``model_point_table.loc[1:1]`` is specified
instead of ``model_point_table.loc[1]``.
Be careful not to accidentally change the original table.
"""
return model_point_table
[docs]def mort_rate(t):
"""Mortality rate to be applied at time t
.. seealso::
* :attr:`mort_table`
* :func:`mort_rate_mth`
"""
result = mort_table[str(min(5, duration(t)))][age(t)]
result.index = model_point().index
return result
[docs]def mort_rate_mth(t):
"""Monthly mortality rate to be applied at time t
.. seealso::
* :attr:`mort_table`
* :func:`mort_rate`
"""
return 1-(1- mort_rate(t))**(1/12)
[docs]def net_cf(t):
"""Net cashflow
Net cashflow for the period from ``t`` to ``t+1`` defined as::
premiums(t) - claims(t) - expenses(t) - commissions(t)
.. seealso::
* :func:`premiums`
* :func:`claims`
* :func:`expenses`
* :func:`commissions`
"""
return premiums(t) - claims(t) - expenses(t) - commissions(t)
[docs]def net_premium_pp():
"""Net premium per policy
The net premium per policy is defined so that
the present value of net premiums equates to the present value of
claims::
pv_claims() / pv_pols_if()
.. seealso::
* :func:`pv_claims`
* :func:`pv_pols_if`
"""
return pv_claims() / pv_pols_if()
[docs]def policy_term():
"""The policy term of the model points.
The ``policy_term`` column of the DataFrame returned by
:func:`model_point`.
"""
return model_point()["policy_term"]
[docs]def pols_death(t):
"""Number of death occurring at time t"""
return pols_if(t) * mort_rate_mth(t)
[docs]def pols_if(t):
"""Number of policies in-force
Number of in-force policies calculated recursively.
The initial value is read from :func:`pols_if_init`.
Subsequent values are defined recursively as::
pols_if(t-1) - pols_lapse(t-1) - pols_death(t-1) - pols_maturity(t)
.. seealso::
* :func:`pols_lapse`
* :func:`pols_death`
* :func:`pols_maturity`
"""
if t==0:
return pols_if_init()
elif t < max_proj_len():
return pols_if(t-1) - pols_lapse(t-1) - pols_death(t-1) - pols_maturity(t)
else:
raise KeyError("t out of range")
[docs]def pols_if_init():
"""Initial Number of Policies In-force
Number of in-force policies at time 0 referenced from :func:`pols_if`.
Defaults to 1.
"""
return pd.Series(1, index=model_point().index)
[docs]def pols_lapse(t):
"""Number of lapse occurring at time t
.. seealso::
* :func:`pols_if`
* :func:`lapse_rate`
"""
return pols_if(t) * (1-(1 - lapse_rate(t))**(1/12))
[docs]def pols_maturity(t):
"""Number of maturing policies
The policy maturity occurs at ``t == 12 * policy_term()``,
after death and lapse during the last period::
pols_if(t-1) - pols_lapse(t-1) - pols_death(t-1)
otherwise ``0``.
"""
return (t == policy_term() * 12) * (pols_if(t-1) - pols_lapse(t-1) - pols_death(t-1))
[docs]def premium_pp():
"""Monthly premium per policy
Monthly premium amount per policy defined as::
round((1 + loading_prem()) * net_premium(), 2)
.. versionchanged:: 0.2.0
The ``t`` parameter is removed.
.. seealso::
* :func:`loading_prem`
* :func:`net_premium_pp`
"""
return np.around((1 + loading_prem()) * net_premium_pp(), 2)
[docs]def premiums(t):
"""Premium income
Premium income during the period from ``t`` to ``t+1`` defined as::
premium_pp(t) * pols_if(t)
.. seealso::
* :func:`premium_pp`
* :func:`pols_if`
"""
return premium_pp() * pols_if(t)
[docs]def proj_len():
"""Projection length in months
Projection length in months defined as::
12 * policy_term() + 1
Since this model carries out projections for all the model points
simultaneously, the projections are actually carried out
from 0 to :attr:`max_proj_len` for all the model points.
.. seealso::
:func:`policy_term`
"""
return 12 * policy_term() + 1
[docs]def pv_claims():
"""Present value of claims
.. seealso::
* :func:`claims`
"""
cl = np.array(list(claims(t) for t in range(max_proj_len()))).transpose()
return cl @ disc_factors()[:max_proj_len()]
[docs]def pv_commissions():
"""Present value of commissions
.. seealso::
* :func:`expenses`
"""
result = np.array(list(commissions(t) for t in range(max_proj_len()))).transpose()
return result @ disc_factors()[:max_proj_len()]
[docs]def pv_expenses():
"""Present value of expenses
.. seealso::
* :func:`expenses`
"""
result = np.array(list(expenses(t) for t in range(max_proj_len()))).transpose()
return result @ disc_factors()[:max_proj_len()]
[docs]def pv_net_cf():
"""Present value of net cashflows.
Defined as::
pv_premiums() - pv_claims() - pv_expenses() - pv_commissions()
.. seealso::
* :func:`pv_premiums`
* :func:`pv_claims`
* :func:`pv_expenses`
* :func:`pv_commissions`
"""
return pv_premiums() - pv_claims() - pv_expenses() - pv_commissions()
[docs]def pv_pols_if():
"""Present value of policies in-force
The discounted sum of the number of in-force policies at each month.
It is used as the annuity factor for calculating :func:`net_premium_pp`.
"""
result = np.array(list(pols_if(t) for t in range(max_proj_len()))).transpose()
return result @ disc_factors()[:max_proj_len()]
[docs]def pv_premiums():
"""Present value of premiums
.. seealso::
* :func:`premiums`
"""
result = np.array(list(premiums(t) for t in range(max_proj_len()))).transpose()
return result @ disc_factors()[:max_proj_len()]
[docs]def result_cf():
"""Result table of cashflows
.. seealso::
* :func:`premiums`
* :func:`claims`
* :func:`expenses`
* :func:`commissions`
* :func:`net_cf`
"""
t_len = range(max_proj_len())
data = {
"Premiums": [sum(premiums(t)) for t in t_len],
"Claims": [sum(claims(t)) for t in t_len],
"Expenses": [sum(expenses(t)) for t in t_len],
"Commissions": [sum(commissions(t)) for t in t_len],
"Net Cashflow": [sum(net_cf(t)) for t in t_len]
}
return pd.DataFrame(data, index=t_len)
[docs]def result_pv():
"""Result table of present value of cashflows
.. seealso::
* :func:`pv_premiums`
* :func:`pv_claims`
* :func:`pv_expenses`
* :func:`pv_commissions`
* :func:`pv_net_cf`
"""
data = {
"PV Premiums": pv_premiums(),
"PV Claims": pv_claims(),
"PV Expenses": pv_expenses(),
"PV Commissions": pv_commissions(),
"PV Net Cashflow": pv_net_cf()
}
return pd.DataFrame(data, index=model_point().index)
[docs]def sex():
"""The sex of the model points
.. note::
This cells is not used by default.
The ``sex`` column of the DataFrame returned by
:func:`model_point`.
"""
return model_point()["sex"]
[docs]def sum_assured():
"""The sum assured of the model points
The ``sum_assured`` column of the DataFrame returned by
:func:`model_point`.
"""
return model_point()["sum_assured"]
# ---------------------------------------------------------------------------
# References
disc_rate_ann = ("DataClient", 2105121422280)
model_point_table = ("DataClient", 2105121417096)
mort_table = ("DataClient", 2105119667144)
np = ("Module", "numpy")
pd = ("Module", "pandas")