CashValue_ME EX1 vs EX4 updated

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"""The main Space in the :mod:`~savings.CashValue_ME` model.
"""The main Space in the :mod:`~savings.CashValue_ME` model.


:mod:`~savings.CashValue_ME.Projection` is the only Space defined
:mod:`~savings.CashValue_ME.Projection` is the only Space defined
in the :mod:`~savings.CashValue_ME` model, and it contains
in the :mod:`~savings.CashValue_ME` model, and it contains
all the logic and data used in the model.
all the logic and data used in the model.


.. rubric:: Parameters and References
.. rubric:: Parameters and References


(In all the sample code below,
(In all the sample code below,
the global variable ``Projection`` refers to the
the global variable ``Projection`` refers to the
:mod:`~savings.CashValue_ME.Projection` Space.)
:mod:`~savings.CashValue_ME.Projection` Space.)


Attributes:
Attributes:


model_point_table: All model points as a DataFrame.
model_point_table: All model points as a DataFrame.
By default, 4 model points are defined.
By default, 4 model points are defined.
The DataFrame has an index named ``point_id``.
The DataFrame has an index named ``point_id``.


* ``spec_id``
* ``spec_id``
* ``age_at_entry``
* ``age_at_entry``
* ``sex``
* ``sex``
* ``policy_term``
* ``policy_term``
* ``policy_count``
* ``policy_count``
* ``sum_assured``
* ``sum_assured``
* ``duration_mth``
* ``duration_mth``
* ``premium_pp``
* ``premium_pp``
* ``av_pp_init``
* ``av_pp_init``


Cells defined in :mod:`~savings.CashValue_ME.Projection`
Cells defined in :mod:`~savings.CashValue_ME.Projection`
with the same names as these columns return
with the same names as these columns return
the corresponding column's values for the selected model point.
the corresponding column's values for the selected model point.


.. code-block::
.. code-block::


>>> Projection.model_poit_table
>>> Projection.model_poit_table
spec_id age_at_entry sex ... premium_pp av_pp_init
spec_id age_at_entry sex ... premium_pp av_pp_init
poind_id ...
poind_id ...
1 A 20 M ... 500000 0
1 A 20 M ... 500000 0
2 B 50 M ... 500000 0
2 B 50 M ... 500000 0
3 C 20 M ... 1000 0
3 C 20 M ... 1000 0
4 D 50 M ... 1000 0
4 D 50 M ... 1000 0


[4 rows x 10 columns]
[4 rows x 10 columns]


The DataFrame is saved in the Excel file *model_point_samples.xlsx*
The DataFrame is saved in the Excel file *model_point_samples.xlsx*
placed in the model folder.
placed in the model folder.
:attr:`model_point_table` is created by
:attr:`model_point_table` is created by
Projection's `new_pandas`_ method,
Projection's `new_pandas`_ method,
so that the DataFrame is saved in the separate file.
so that the DataFrame is saved in the separate file.
The DataFrame has the injected attribute
The DataFrame has the injected attribute
of ``_mx_dataclident``::
of ``_mx_dataclident``::


>>> Projection.model_point_table._mx_dataclient
>>> Projection.model_point_table._mx_dataclient
<PandasData path='model_point_table_samples.xlsx' filetype='excel'>
<PandasData path='model_point_table_samples.xlsx' filetype='excel'>


.. seealso::
.. seealso::


* :func:`model_point`
* :func:`model_point`
* :func:`age_at_entry`
* :func:`age_at_entry`
* :func:`sex`
* :func:`sex`
* :func:`policy_term`
* :func:`policy_term`
* :func:`pols_if_init`
* :func:`pols_if_init`
* :func:`sum_assured`
* :func:`sum_assured`
* :func:`duration_mth`
* :func:`duration_mth`
* :func:`premium_pp`
* :func:`premium_pp`
* :func:`av_pp_init`
* :func:`av_pp_init`


model_point_10000: Alternative model point table
model_point_10000: Alternative model point table


This model point table contains 10000 model points and
This model point table contains 10000 model points and
is saved as the Excel file *model_point_10000.xlsx*
is saved as the Excel file *model_point_10000.xlsx*
placed in the folder. To use this table, assign it to
placed in the folder. To use this table, assign it to
:attr:`model_point_table`::
:attr:`model_point_table`::


>>> Projection.model_point_table = Projection.model_point_10000
>>> Projection.model_point_table = Projection.model_point_10000




disc_rate_ann: Annual discount rates by duration as a pandas Series.
disc_rate_ann: Annual discount rates by duration as a pandas Series.


.. code-block::
.. code-block::


>>> Projection.disc_rate_ann
>>> Projection.disc_rate_ann
year
year
0 0.00000
0 0.00000
1 0.00555
1 0.00555
2 0.00684
2 0.00684
3 0.00788
3 0.00788
4 0.00866
4 0.00866


146 0.03025
146 0.03025
147 0.03033
147 0.03033
148 0.03041
148 0.03041
149 0.03049
149 0.03049
150 0.03056
150 0.03056
Name: disc_rate_ann, Length: 151, dtype: float64
Name: disc_rate_ann, Length: 151, dtype: float64


The Series is saved in the Excel file *disc_rate_ann.xlsx*
The Series is saved in the Excel file *disc_rate_ann.xlsx*
placed in the model folder.
placed in the model folder.
:attr:`disc_rate_ann` is created by
:attr:`disc_rate_ann` is created by
Projection's `new_pandas`_ method,
Projection's `new_pandas`_ method,
so that the Series is saved in the separate file.
so that the Series is saved in the separate file.
The Series has the injected attribute
The Series has the injected attribute
of ``_mx_dataclident``::
of ``_mx_dataclident``::


>>> Projection.disc_rate_ann._mx_dataclient
>>> Projection.disc_rate_ann._mx_dataclient
<PandasData path='disc_rate_ann.xlsx' filetype='excel'>
<PandasData path='disc_rate_ann.xlsx' filetype='excel'>


.. seealso::
.. seealso::


* :func:`disc_rate_mth`
* :func:`disc_rate_mth`
* :func:`disc_factors`
* :func:`disc_factors`


mort_table: Mortality table by age and duration as a DataFrame.
mort_table: Mortality table by age and duration as a DataFrame.
See *basic_term_sample.xlsx* included in this library
See *basic_term_sample.xlsx* included in this library
for how the sample mortality rates are created.
for how the sample mortality rates are created.


.. code-block::
.. code-block::


>>> Projection.mort_table
>>> Projection.mort_table
0 1 2 3 4 5
0 1 2 3 4 5
Age
Age
18 0.000231 0.000254 0.000280 0.000308 0.000338 0.000372
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
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
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
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
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
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
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
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
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
120 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000


[103 rows x 6 columns]
[103 rows x 6 columns]


The DataFrame is saved in the Excel file *mort_table.xlsx*
The DataFrame is saved in the Excel file *mort_table.xlsx*
placed in the model folder.
placed in the model folder.
:attr:`mort_table` is created by
:attr:`mort_table` is created by
Projection's `new_pandas`_ method,
Projection's `new_pandas`_ method,
so that the DataFrame is saved in the separate file.
so that the DataFrame is saved in the separate file.
The DataFrame has the injected attribute
The DataFrame has the injected attribute
of ``_mx_dataclident``::
of ``_mx_dataclident``::


>>> Projection.mort_table._mx_dataclient
>>> Projection.mort_table._mx_dataclient
<PandasData path='mort_table.xlsx' filetype='excel'>
<PandasData path='mort_table.xlsx' filetype='excel'>


.. seealso::
.. seealso::


* :func:`mort_rate`
* :func:`mort_rate`
* :func:`mort_rate_mth`
* :func:`mort_rate_mth`


std_norm_rand: Random numbers drawn from the standard normal distribution
std_norm_rand: Random numbers drawn from the standard normal distribution


A Series of random numbers drawn from the standard normal distribution
A Series of random numbers drawn from the standard normal distribution
indexed with ``scen_id`` and ``t``.
indexed with ``scen_id`` and ``t``.
Used for generating investment returns. See :func:`inv_return_table`.
Used for generating investment returns. See :func:`inv_return_table`.


scen_id: Selected scenario ID
scen_id: Selected scenario ID


An integer indicating the selected scenario ID.
An integer indicating the selected scenario ID.
:attr:`scen_id` is referenced in by :func:`inv_return_mth`
:attr:`scen_id` is referenced in by :func:`inv_return_mth`
as one of the keys to select a scenario from :attr:`std_norm_rand`.
as one of the keys to select a scenario from :attr:`std_norm_rand`.


surr_charge_table: Surrender charge rates by duration
surr_charge_table: Surrender charge rates by duration


A DataFrame of multiple patterns of surrender charge rates by duration.
A DataFrame of multiple patterns of surrender charge rates by duration.
The column labels indicate :func:`surr_charge_id`.
The column labels indicate :func:`surr_charge_id`.
By default, ``"type_1"``, ``"type_2"`` and ``"type_3"`` are defined.
By default, ``"type_1"``, ``"type_2"`` and ``"type_3"`` are defined.


product_spec_table: Table of product specs
product_spec_table: Table of product specs


A DataFrame of product spec parameters by ``spec_id``.
A DataFrame of product spec parameters by ``spec_id``.
:attr:`model_point_table` and :attr:`product_spec_table` columns
:attr:`model_point_table` and :attr:`product_spec_table` columns
are joined in :func:`model_point_table_ext`,
are joined in :func:`model_point_table_ext`,
and the :attr:`product_spec_table` columns become part
and the :attr:`product_spec_table` columns become part
of the model point attributes.
of the model point attributes.
The :attr:`product_spec_table` columns are read
The :attr:`product_spec_table` columns are read
by the Cells with the same names as the columns:
by the Cells with the same names as the columns:


* :func:`premium_type`
* :func:`premium_type`
* :func:`has_surr_charge`
* :func:`has_surr_charge`
* :func:`surr_charge_id`
* :func:`surr_charge_id`
* :func:`load_prem_rate`
* :func:`load_prem_rate`
* :func:`is_wl`
* :func:`is_wl`


.. code-block::
.. code-block::


>>> Projection.product_spec_table
>>> Projection.product_spec_table
premium_type has_surr_charge surr_charge_id load_prem_rate is_wl
premium_type has_surr_charge surr_charge_id load_prem_rate is_wl
spec_id
spec_id
A SINGLE False NaN 0.10 False
A SINGLE False NaN 0.10 False
B SINGLE True type_1 0.00 False
B SINGLE True type_1 0.00 False
C LEVEL False NaN 0.10 True
C LEVEL False NaN 0.10 True
D LEVEL True type_3 0.05 True
D LEVEL True type_3 0.05 True




np: The `numpy`_ module.
np: The `numpy`_ module.
pd: The `pandas`_ module.
pd: The `pandas`_ module.


.. _numpy:
.. _numpy:
https://numpy.org/
https://numpy.org/


.. _pandas:
.. _pandas:
https://pandas.pydata.org/
https://pandas.pydata.org/


.. _new_pandas:
.. _new_pandas:
https://docs.modelx.io/en/latest/reference/space/generated/modelx.core.space.UserSpace.new_pandas.html
https://docs.modelx.io/en/latest/reference/space/generated/modelx.core.space.UserSpace.new_pandas.html


"""
"""


from modelx.serialize.jsonvalues import *
from modelx.serialize.jsonvalues import *


_formula = None
_formula = None


_bases = []
_bases = []


_allow_none = None
_allow_none = None


_spaces = []
_spaces = []


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


def age(t):
def age(t):
"""The attained age at time t.
"""The attained age at time t.


Defined as::
Defined as::


age_at_entry() + duration(t)
age_at_entry() + duration(t)


.. seealso::
.. seealso::


* :func:`age_at_entry`
* :func:`age_at_entry`
* :func:`duration`
* :func:`duration`


"""
"""
return age_at_entry() + duration(t)
return age_at_entry() + duration(t)




def age_at_entry():
def age_at_entry():
"""The age at entry of the model points
"""The age at entry of the model points


The ``age_at_entry`` column of the DataFrame returned by
The ``age_at_entry`` column of the DataFrame returned by
:func:`model_point`.
:func:`model_point`.
"""
"""
return model_point()["age_at_entry"]
return model_point()["age_at_entry"].values




def av_at(t, timing):
def av_at(t, timing):
"""Account value in-force
"""Account value in-force


:func:`av_at(t, timing)<av_at>` calculates
:func:`av_at(t, timing)<av_at>` calculates
the total amount of account value at time ``t`` for the policies represented
the total amount of account value at time ``t`` for the policies represented
by a model point.
by a model point.


At each ``t``, the events that change the account value balance
At each ``t``, the events that change the account value balance
occur in the following order:
occur in the following order:


* Maturity
* Maturity
* New business and premium payment
* New business and premium payment
* Fee deduction
* Fee deduction


The second parameter ``timing`` takes a string to
The second parameter ``timing`` takes a string to
indicate the timing of the account value, which is either
indicate the timing of the account value, which is either
``"BEF_MAT"``, ``"BEF_NB"`` or ``"BEF_FEE"``.
``"BEF_MAT"``, ``"BEF_NB"`` or ``"BEF_FEE"``.




.. rubric:: BEF_MAT
.. rubric:: BEF_MAT


The amount of account value before maturity, defined as::
The amount of account value before maturity, defined as::


av_pp_at(t, "BEF_PREM") * pols_if_at(t, "BEF_MAT")
av_pp_at(t, "BEF_PREM") * pols_if_at(t, "BEF_MAT")


.. rubric:: BEF_NB
.. rubric:: BEF_NB


The amount of account value before new business after maturity,
The amount of account value before new business after maturity,
defined as::
defined as::


av_pp_at(t, "BEF_PREM") * pols_if_at(t, "BEF_NB")
av_pp_at(t, "BEF_PREM") * pols_if_at(t, "BEF_NB")


.. rubric:: BEF_FEE
.. rubric:: BEF_FEE


The amount of account value before lapse and death after new business,
The amount of account value before lapse and death after new business,
defined as::
defined as::


av_pp_at(t, "BEF_FEE") * pols_if_at(t, "BEF_DECR")
av_pp_at(t, "BEF_FEE") * pols_if_at(t, "BEF_DECR")




.. seealso::
.. seealso::
* :func:`pols_if_at`
* :func:`pols_if_at`
* :func:`av_pp_at`
* :func:`av_pp_at`




"""
"""
if timing == "BEF_MAT":
if timing == "BEF_MAT":
return av_pp_at(t, "BEF_PREM") * pols_if_at(t, "BEF_MAT")
return av_pp_at(t, "BEF_PREM") * pols_if_at(t, "BEF_MAT")


elif timing == "BEF_NB":
elif timing == "BEF_NB":
return av_pp_at(t, "BEF_PREM") * pols_if_at(t, "BEF_NB")
return av_pp_at(t, "BEF_PREM") * pols_if_at(t, "BEF_NB")


elif timing == "BEF_FEE":
elif timing == "BEF_FEE":
return av_pp_at(t, "BEF_FEE") * pols_if_at(t, "BEF_DECR")
return av_pp_at(t, "BEF_FEE") * pols_if_at(t, "BEF_DECR")


else:
else:
raise ValueError("invalid timing")
raise ValueError("invalid timing")




def av_change(t):
def av_change(t):
"""Change in account value
"""Change in account value


Change in account value during each period, defined as::
Change in account value during each period, defined as::


av_at(t+1, 'BEF_MAT') - av_at(t, 'BEF_MAT')
av_at(t+1, 'BEF_MAT') - av_at(t, 'BEF_MAT')


.. seealso::
.. seealso::


* :func:`net_cf`
* :func:`net_cf`


"""
"""
return av_at(t+1, 'BEF_MAT') - av_at(t, 'BEF_MAT')
return av_at(t+1, 'BEF_MAT') - av_at(t, 'BEF_MAT')




def av_pp_at(t, timing):
def av_pp_at(t, timing):
"""Account value per policy
"""Account value per policy


:func:`av_at(t, timing)<av_at>` calculates
:func:`av_at(t, timing)<av_at>` calculates
the total amount of account value at time ``t`` for the policies in-force.
the total amount of account value at time ``t`` for the policies in-force.


At each ``t``, the events that change the account value balance
At each ``t``, the events that change the account value balance
occur in the following order:
occur in the following order:


* Premium payment
* Premium payment
* Fee deduction
* Fee deduction


Investment income is assumed to be earned throughout each month,
Investment income is assumed to be earned throughout each month,
so at the middle of the month when death and lapse occur,
so at the middle of the month when death and lapse occur,
half the investment income for the month is credited.
half the investment income for the month is credited.


The second parameter ``timing`` takes a string to
The second parameter ``timing`` takes a string to
indicate the timing of the account value, which is either
indicate the timing of the account value, which is either
``"BEF_PREM"``, ``"BEF_FEE"``, ``"BEF_INV"`` or ``"MID_MTH"``.
``"BEF_PREM"``, ``"BEF_FEE"``, ``"BEF_INV"`` or ``"MID_MTH"``.




.. rubric:: BEF_PREM
.. rubric:: BEF_PREM


Account value before premium payment.
Account value before premium payment.
At the start of the projection (i.e. when ``t=0``),
At the start of the projection (i.e. when ``t=0``),
the account value is set to :func:`av_pp_init`.
the account value is set to :func:`av_pp_init`.


.. rubric:: BEF_FEE
.. rubric:: BEF_FEE


Account value after premium payment before fee deduction
Account value after premium payment before fee deduction




.. rubric:: BEF_INV
.. rubric:: BEF_INV


Account value after fee deduction before crediting investemnt return
Account value after fee deduction before crediting investemnt return


.. rubric:: MID_MTH
.. rubric:: MID_MTH


Account value at middle of month (``t+0.5``) when
Account value at middle of month (``t+0.5``) when
half the investment retun for the month is credited
half the investment retun for the month is credited




.. seealso::
.. seealso::
* :func:`av_pp_init`
* :func:`av_pp_init`
* :func:`inv_income_pp`
* :func:`inv_income_pp`
* :func:`prem_to_av_pp`
* :func:`prem_to_av_pp`
* :func:`maint_fee_pp`
* :func:`maint_fee_pp`
* :func:`coi_pp`
* :func:`coi_pp`
* :func:`av_at`
* :func:`av_at`


"""
"""
if timing == "BEF_PREM":
if timing == "BEF_PREM":
if t == 0:
if t == 0:
return av_pp_init()
return av_pp_init()
else:
else:
return av_pp_at(t-1, "BEF_INV") + inv_income_pp(t-1)
return av_pp_at(t-1, "BEF_INV") + inv_income_pp(t-1)


elif timing == "BEF_FEE":
elif timing == "BEF_FEE":
return av_pp_at(t, "BEF_PREM") + prem_to_av_pp(t)
return av_pp_at(t, "BEF_PREM") + prem_to_av_pp(t)


elif timing == "BEF_INV":
elif timing == "BEF_INV":
return av_pp_at(t, "BEF_FEE") - maint_fee_pp(t) - coi_pp(t)
return av_pp_at(t, "BEF_FEE") - maint_fee_pp(t) - coi_pp(t)


elif timing == "MID_MTH":
elif timing == "MID_MTH":
return av_pp_at(t, "BEF_INV") + 0.5 * inv_income_pp(t)
return av_pp_at(t, "BEF_INV") + 0.5 * inv_income_pp(t)


else:
else:
raise ValueError("invalid timing")
raise ValueError("invalid timing")




def av_pp_init():
def av_pp_init():
"""Initial account value per policy
"""Initial account value per policy


For existing business at time ``0``,
For existing business at time ``0``,
returns initial per-policy accout value read from
returns initial per-policy accout value read from
the ``av_pp_init`` column in :func:`model_point`.
the ``av_pp_init`` column in :func:`model_point`.
For new business, 0 should be entered in the column.
For new business, 0 should be entered in the column.


.. seealso::
.. seealso::


* :func:`model_point`
* :func:`model_point`
* :func:`av_pp_at`
* :func:`av_pp_at`


"""
"""
return model_point()["av_pp_init"]
return model_point()["av_pp_init"].values




def check_av_roll_fwd():
def check_av_roll_fwd():
"""Check account value roll-forward
"""Check account value roll-forward


Returns ``Ture`` if ``av_at(t+1, "BEF_NB")`` equates to
Returns ``Ture`` if ``av_at(t+1, "BEF_NB")`` equates to
the following expression for all ``t``, otherwise returns ``False``::
the following expression for all ``t``, otherwise returns ``False``::


av_at(t, "BEF_MAT")
av_at(t, "BEF_MAT")
+ prem_to_av(t)
+ prem_to_av(t)
- maint_fee(t)
- maint_fee(t)
- coi(t)
- coi(t)
+ inv_income(t)
+ inv_income(t)
- claims_from_av(t, "DEATH")
- claims_from_av(t, "DEATH")
- claims_from_av(t, "LAPSE")
- claims_from_av(t, "LAPSE")
- claims_from_av(t, "MATURITY"))
- claims_from_av(t, "MATURITY"))


.. seealso::
.. seealso::


* :func:`av_at`
* :func:`av_at`
* :func:`prem_to_av`
* :func:`prem_to_av`
* :func:`maint_fee`
* :func:`maint_fee`
* :func:`coi`
* :func:`coi`
* :func:`inv_income`
* :func:`inv_income`
* :func:`claims_from_av`
* :func:`claims_from_av`


"""
"""
for t in range(max_proj_len()):
for t in range(max_proj_len()):


av = (av_at(t, "BEF_MAT")
av = (av_at(t, "BEF_MAT")
+ prem_to_av(t)
+ prem_to_av(t)
- maint_fee(t)
- maint_fee(t)
- coi(t)
- coi(t)
+ inv_income(t)
+ inv_income(t)
- claims_from_av(t, "DEATH")
- claims_from_av(t, "DEATH")
- claims_from_av(t, "LAPSE")
- claims_from_av(t, "LAPSE")
- claims_from_av(t, "MATURITY"))
- claims_from_av(t, "MATURITY"))


if np.all(np.isclose(av_at(t+1, "BEF_MAT"), av)):
if np.all(np.isclose(av_at(t+1, "BEF_MAT"), av)):
continue
continue
else:
else:
return False
return False


return True
return True




def check_margin():
def check_margin():
"""Check consistency between net cashflow and margins
"""Check consistency between net cashflow and margins


Returns ``True`` if :func:`net_cf` equates to the sum of
Returns ``True`` if :func:`net_cf` equates to the sum of
:func:`margin_expense` and :func:`margin_mortality` for all ``t``,
:func:`margin_expense` and :func:`margin_mortality` for all ``t``,
otherwise, returns ``False``.
otherwise, returns ``False``.


.. seealso::
.. seealso::


* :func:`net_cf`
* :func:`net_cf`
* :func:`margin_expense`
* :func:`margin_expense`
* :func:`margin_mortality`
* :func:`margin_mortality`


"""
"""
res = []
res = []
for t in range(max_proj_len()):
for t in range(max_proj_len()):
res.append(np.all(np.isclose(net_cf(t), margin_expense(t) + margin_mortality(t))))
res.append(np.all(np.isclose(net_cf(t), margin_expense(t) + margin_mortality(t))))


return all(res)
return all(res)




def check_pv_net_cf():
def check_pv_net_cf():
"""Check present value summation
"""Check present value summation


Check if the present value of :func:`net_cf` matches the
Check if the present value of :func:`net_cf` matches the
sum of the present values of each cashflow.
sum of the present values of each cashflow.
Returns the check result as :obj:`True` or :obj:`False`.
Returns the check result as :obj:`True` or :obj:`False`.


.. seealso::
.. seealso::


* :func:`net_cf`
* :func:`net_cf`
* :func:`pv_net_cf`
* :func:`pv_net_cf`


"""
"""
cfs = np.array(list(net_cf(t) for t in range(max_proj_len()))).transpose()
cfs = np.array(list(net_cf(t) for t in range(max_proj_len()))).transpose()
pvs = cfs @ disc_factors()[:max_proj_len()]
pvs = cfs @ disc_factors()[:max_proj_len()]


return np.all(np.isclose(pvs, pv_net_cf()))
return np.all(np.isclose(pvs, pv_net_cf()))




def claim_net_pp(t, kind):
def claim_net_pp(t, kind):


if kind == "DEATH":
if kind == "DEATH":
return claim_pp(t, "DEATH") - av_pp_at(t, "MID_MTH")
return claim_pp(t, "DEATH") - av_pp_at(t, "MID_MTH")


elif kind == "LAPSE":
elif kind == "LAPSE":
return 0
return 0


elif kind == "MATURITY":
elif kind == "MATURITY":
return claim_pp(t, "MATURITY") - av_pp_at(t, "BEF_PREM")
return claim_pp(t, "MATURITY") - av_pp_at(t, "BEF_PREM")


else:
else:
raise ValueError("invalid kind")
raise ValueError("invalid kind")




def claim_pp(t, kind):
def claim_pp(t, kind):
"""Claim per policy
"""Claim per policy


The claim amount per policy. The second parameter
The claim amount per policy. The second parameter
is to indicate the type of the claim, and
is to indicate the type of the claim, and
it takes a string, which is either ``"DEATH"``, ``"LAPSE"`` or ``"MATURITY"``.
it takes a string, which is either ``"DEATH"``, ``"LAPSE"`` or ``"MATURITY"``.


The death benefit as denoted by ``"DEATH"``, is
The death benefit as denoted by ``"DEATH"``, is
the greater of :func:`sum_assured` and
the greater of :func:`sum_assured` and
mid-month account value (:func:`av_pp_at(t, "MID_MTH")<av_pp_at>`).
mid-month account value (:func:`av_pp_at(t, "MID_MTH")<av_pp_at>`).


The surrender benefit as denoted by ``"LAPSE"`` and
The surrender benefit as denoted by ``"LAPSE"`` and
the maturity benefit as denoted by ``"MATURITY"`` are
the maturity benefit as denoted by ``"MATURITY"`` are
equal to the mid-month account value.
equal to the mid-month account value.


.. seealso::
.. seealso::


* :func:`sum_assured`
* :func:`sum_assured`
* :func:`av_pp_at`
* :func:`av_pp_at`


"""
"""


if kind == "DEATH":
if kind == "DEATH":
return np.maximum(sum_assured(), av_pp_at(t, "MID_MTH"))
return np.maximum(sum_assured(), av_pp_at(t, "MID_MTH"))


elif kind == "LAPSE":
elif kind == "LAPSE":
return av_pp_at(t, "MID_MTH")
return av_pp_at(t, "MID_MTH")


elif kind == "MATURITY":
elif kind == "MATURITY":
return np.maximum(sum_assured(), av_pp_at(t, "BEF_PREM"))
return np.maximum(sum_assured(), av_pp_at(t, "BEF_PREM"))


else:
else:
raise ValueError("invalid kind")
raise ValueError("invalid kind")




def claims(t, kind=None):
def claims(t, kind=None):
"""Claims
"""Claims


The claim amount during the period from ``t`` to ``t+1``.
The claim amount during the period from ``t`` to ``t+1``.
The optional second parameter is for indicating the type of the claim, and
The optional second parameter is for indicating the type of the claim, and
it takes a string, which is either ``"DEATH"``, ``"LAPSE"`` or ``"MATURITY"``,
it takes a string, which is either ``"DEATH"``, ``"LAPSE"`` or ``"MATURITY"``,
or defaults to ``None`` to indicate the total of all the types of claims
or defaults to ``None`` to indicate the total of all the types of claims
during the period.
during the period.




The death benefit as denoted by ``"DEATH"`` is defined as::
The death benefit as denoted by ``"DEATH"`` is defined as::


claim_pp(t) * pols_death(t)
claim_pp(t) * pols_death(t)


The surrender benefit as denoted by ``"LAPSE"`` is defined as::
The surrender benefit as denoted by ``"LAPSE"`` is defined as::


claims_from_av(t, "LAPSE") - surr_charge(t)
claims_from_av(t, "LAPSE") - surr_charge(t)


The maturity benefit as denoted by ``"MATURITY"`` is defined as::
The maturity benefit as denoted by ``"MATURITY"`` is defined as::


claims_from_av(t, "MATURITY")
claims_from_av(t, "MATURITY")


.. seealso::
.. seealso::


* :func:`claim_pp`
* :func:`claim_pp`
* :func:`pols_death`
* :func:`pols_death`
* :func:`claims_from_av`
* :func:`claims_from_av`
* :func:`surr_charge`
* :func:`surr_charge`


"""
"""


if kind == "DEATH":
if kind == "DEATH":
return claim_pp(t, "DEATH") * pols_death(t)
return claim_pp(t, "DEATH") * pols_death(t)


elif kind == "LAPSE":
elif kind == "LAPSE":
return claims_from_av(t, "LAPSE") - surr_charge(t)
return claims_from_av(t, "LAPSE") - surr_charge(t)


elif kind == "MATURITY":
elif kind == "MATURITY":
return claim_pp(t, "MATURITY") * pols_maturity(t)
return claim_pp(t, "MATURITY") * pols_maturity(t)


elif kind is None:
elif kind is None:
return sum(claims[t, k] for k in ["DEATH", "LAPSE", "MATURITY"])
return sum(claims[t, k] for k in ["DEATH", "LAPSE", "MATURITY"])


else:
else:
raise ValueError("invalid kind")
raise ValueError("invalid kind")




def claims_from_av(t, kind):
def claims_from_av(t, kind):
"""Account value taken out to pay claim
"""Account value taken out to pay claim


The part of the claim amount that is paid from account value.
The part of the claim amount that is paid from account value.
The second parameter takes a string indicating the type of the claim,
The second parameter takes a string indicating the type of the claim,
which is either ``"DEATH"``, ``"LAPSE"`` or ``"MATURITY"``.
which is either ``"DEATH"``, ``"LAPSE"`` or ``"MATURITY"``.




Death benefit is denoted by ``"DEATH"``, is defined as::
Death benefit is denoted by ``"DEATH"``, is defined as::


av_pp_at(t, "MID_MTH") * pols_death(t)
av_pp_at(t, "MID_MTH") * pols_death(t)


When the account value is greater than the death benefit,
When the account value is greater than the death benefit,
the death benefit equates to the account value.
the death benefit equates to the account value.


Surrender benefit as denoted by ``"LAPSE"`` is defined as::
Surrender benefit as denoted by ``"LAPSE"`` is defined as::


av_pp_at(t, "MID_MTH") * pols_lapse(t)
av_pp_at(t, "MID_MTH") * pols_lapse(t)


As the surrender benefit is defined as account value less surrender
As the surrender benefit is defined as account value less surrender
charge, when there is no surrender charge the surrender benefit
charge, when there is no surrender charge the surrender benefit
equates to the account value.
equates to the account value.


Maturity benefit as denoted by ``"MATURITY"`` is defined as::
Maturity benefit as denoted by ``"MATURITY"`` is defined as::


av_pp_at(t, "BEF_PREM") * pols_maturity(t)
av_pp_at(t, "BEF_PREM") * pols_maturity(t)


By default, the maturity benefit equates to the account value
By default, the maturity benefit equates to the account value
of maturing policies.
of maturing policies.


.. seealso::
.. seealso::


* :func:`av_pp_at`
* :func:`av_pp_at`
* :func:`pols_death`
* :func:`pols_death`
* :func:`pols_lapse`
* :func:`pols_lapse`
* :func:`pols_maturity`
* :func:`pols_maturity`


"""
"""


if kind == "DEATH":
if kind == "DEATH":
return av_pp_at(t, "MID_MTH") * pols_death(t)
return av_pp_at(t, "MID_MTH") * pols_death(t)


elif kind == "LAPSE":
elif kind == "LAPSE":
return av_pp_at(t, "MID_MTH") * pols_lapse(t)
return av_pp_at(t, "MID_MTH") * pols_lapse(t)


elif kind == "MATURITY":
elif kind == "MATURITY":
return av_pp_at(t, "BEF_PREM") * pols_maturity(t)
return av_pp_at(t, "BEF_PREM") * pols_maturity(t)


else:
else:
raise ValueError("invalid kind")
raise ValueError("invalid kind")




def claims_over_av(t, kind):
def claims_over_av(t, kind):
"""Claim in excess of account value
"""Claim in excess of account value


The amount of death benefits in excess of account value.
The amount of death benefits in excess of account value.
:func:`coi` net of this amount represents mortality margin.
:func:`coi` net of this amount represents mortality margin.


.. seealso::
.. seealso::


* :func:`margin_mortality`
* :func:`margin_mortality`
* :func:`coi`
* :func:`coi`


"""
"""
return claims(t, kind) - claims_from_av(t, kind)
return claims(t, kind) - claims_from_av(t, kind)




def coi(t):
def coi(t):
"""Cost of insurance charges
"""Cost of insurance charges


The cost of insurance charges deducted from acccount values
The cost of insurance charges deducted from acccount values
each period.
each period.


.. seealso::
.. seealso::


* :func:`pols_if_at`
* :func:`pols_if_at`
* :func:`coi_pp`
* :func:`coi_pp`


"""
"""
return coi_pp(t) * pols_if_at(t, "BEF_DECR")
return coi_pp(t) * pols_if_at(t, "BEF_DECR")




def coi_pp(t):
def coi_pp(t):
"""Cost of insurance charges per policy
"""Cost of insurance charges per policy


The cost of insurance charges per policy.
The cost of insurance charges per policy.
Defined as the coi charge rate times net amount at risk per policy.
Defined as the coi charge rate times net amount at risk per policy.


.. seealso::
.. seealso::


* :func:`coi`
* :func:`coi`
* :func:`coi_rate`
* :func:`coi_rate`
* :func:`net_amt_at_risk`
* :func:`net_amt_at_risk`


"""
"""
return coi_rate(t) * net_amt_at_risk(t)
return coi_rate(t) * net_amt_at_risk(t)




def coi_rate(t):
def coi_rate(t):
"""Cost of insurance rate per account value
"""Cost of insurance rate per account value


The cost of insuranc rate per account value per month.
The cost of insuranc rate per account value per month.
By default, it is set to 1.1 times the monthly mortality rate.
By default, it is set to 1.1 times the monthly mortality rate.


.. seealso::
.. seealso::


* :func:`mort_rate_mth`
* :func:`mort_rate_mth`
* :func:`coi_pp`
* :func:`coi_pp`
* :func:`coi_rate`
* :func:`coi_rate`


"""
"""
return 0 #1.1 * mort_rate_mth(t)
return 0 #1.1 * mort_rate_mth(t)




def commissions(t):
def commissions(t):
"""Commissions
"""Commissions


By default, 100% premiums for the first year, 0 otherwise.
By default, 100% premiums for the first year, 0 otherwise.


.. seealso::
.. seealso::


* :func:`premiums`
* :func:`premiums`
* :func:`duration`
* :func:`duration`


"""
"""
return 0.05 * premiums(t)
return 0.05 * premiums(t)




def disc_factors():
def disc_factors(t):
"""Discount factors.
"""Discount factors.


Vector of the discount factors as a Numpy array. Used for calculating
Vector of the discount factors as a Numpy array. Used for calculating
the present values of cashflows.
the present values of cashflows.


.. seealso::
.. seealso::


:func:`disc_rate_mth`
:func:`disc_rate_mth`
"""
"""
return np.array(list((1 + disc_rate_mth()[t])**(-t) for t in range(max_proj_len())))
return (1 + disc_rate_mth(t))**(-t)




def disc_rate_mth():
def disc_rate_mth(t):
"""Monthly discount rate
"""Monthly discount rate


Nummpy array of monthly discount rates from time 0 to :func:`max_proj_len` - 1
Nummpy array of monthly discount rates from time 0 to :func:`max_proj_len` - 1
defined as::
defined as::


(1 + disc_rate_ann)**(1/12) - 1
(1 + disc_rate_ann)**(1/12) - 1


.. seealso::
.. seealso::


:func:`disc_rate_ann`
:func:`disc_rate_ann`


"""
"""
return np.array(list((1 + disc_rate_ann[t//12])**(1/12) - 1 for t in range(max_proj_len())))
return (1 + disc_rate_ann[t//12])**(1/12) - 1




def duration(t):
def duration(t):
"""Duration of model points at ``t`` in years
"""Duration of model points at ``t`` in years


.. seealso:: :func:`duration_mth`
.. seealso:: :func:`duration_mth`


"""
"""
return duration_mth(t) //12
return duration_mth(t) //12




def duration_mth(t):
def duration_mth(t):
"""Duration of model points at ``t`` in months
"""Duration of model points at ``t`` in months


Indicates how many months the policies have been in-force at ``t``.
Indicates how many months the policies have been in-force at ``t``.
The initial values at time 0 are read from the ``duration_mth`` column in
The initial values at time 0 are read from the ``duration_mth`` column in
:attr:`model_point_table` through :func:`model_point`.
:attr:`model_point_table` through :func:`model_point`.
Increments by 1 as ``t`` increments.
Increments by 1 as ``t`` increments.
Negative values of :func:`duration_mth` indicate future new business
Negative values of :func:`duration_mth` indicate future new business
policies. For example, If the :func:`duration_mth` is
policies. For example, If the :func:`duration_mth` is
-15 at time 0, the model point is issued at ``t=15``.
-15 at time 0, the model point is issued at ``t=15``.


.. seealso:: :func:`model_point`
.. seealso:: :func:`model_point`


"""
"""


if t == 0:
if t == 0:
return model_point()['duration_mth']
return model_point()['duration_mth'].values
else:
else:
return duration_mth(t-1) + 1
return duration_mth(t-1) + 1




def expense_acq():
def expense_acq():
"""Acquisition expense per policy
"""Acquisition expense per policy


``5000`` by default.
``5000`` by default.
"""
"""
return 5000
return 5000




def expense_maint():
def expense_maint():
"""Annual maintenance expense per policy
"""Annual maintenance expense per policy


``500`` by default.
``500`` by default.
"""
"""
return 500
return 500




def expenses(t):
def expenses(t):
"""Expenses
"""Expenses


Expenses during the period from ``t`` to ``t+1``
Expenses during the period from ``t`` to ``t+1``
defined as the sum of acquisition expenses and maintenance expenses.
defined as the sum of acquisition expenses and maintenance expenses.
The acquisition expenses are modeled as :func:`expense_acq`
The acquisition expenses are modeled as :func:`expense_acq`
times :func:`pols_new_biz`.
times :func:`pols_new_biz`.
The maintenance expenses are modeled as :func:`expense_maint`
The maintenance expenses are modeled as :func:`expense_maint`
times :func:`inflation_factor` times :func:`pols_if_at` before
times :func:`inflation_factor` times :func:`pols_if_at` before
decrement.
decrement.


.. seealso::
.. seealso::


* :func:`expense_acq`
* :func:`expense_acq`
* :func:`expense_maint`
* :func:`expense_maint`
* :func:`inflation_factor`
* :func:`inflation_factor`
* :func:`pols_new_biz`
* :func:`pols_new_biz`
* :func:`pols_if_at`
* :func:`pols_if_at`
"""
"""


return expense_acq() * pols_new_biz(t) \
return expense_acq() * pols_new_biz(t) \
+ pols_if_at(t, "BEF_DECR") * expense_maint()/12 * inflation_factor(t)
+ pols_if_at(t, "BEF_DECR") * expense_maint()/12 * inflation_factor(t)




def formula_option_put(t):
def formula_option_put(t):
"""
"""
S: prem_to_av
S: prem_to_av
X: claims
X: claims
sigma: 0.03
sigma: 0.03
r: 0.02
r: 0.02


"""
"""
mps = model_point_table_ext()
mps = model_point_table_ext()
cond = mps['policy_term'] * 12 == t
cond = mps['policy_term'] * 12 == t
mps = mps.loc[cond]
mps = mps.loc[cond]


T = t / 12
T = t / 12
S = av_at(0, 'BEF_FEE')[:, 1][cond]
S = av_at(0, 'BEF_FEE')[:, 1][cond]
X = (sum_assured() * pols_maturity(t))[:, 1][cond]
X = (sum_assured() * pols_maturity(t))[:, 1][cond]
sigma = 0.03
sigma = 0.03
r = 0.02
r = 0.02
N = stats.norm.cdf
N = stats.norm.cdf
e = np.exp
e = np.exp


d1 = (np.log(S/X) + (r + 0.5 * sigma**2) * T) / (sigma * np.sqrt(T))
d1 = (np.log(S/X) + (r + 0.5 * sigma**2) * T) / (sigma * np.sqrt(T))
d2 = d1 - sigma * np.sqrt(T)
d2 = d1 - sigma * np.sqrt(T)


return X * e(-r*T) * N(-d2) - S * N(-d1)
return X * e(-r*T) * N(-d2) - S * N(-d1)




def has_surr_charge():
def has_surr_charge():
"""Whether surrender charge applies
"""Whether surrender charge applies


``True`` if surrender charge on account value applies upon lapse,
``True`` if surrender charge on account value applies upon lapse,
``False`` if other wise.
``False`` if other wise.
By default, the value is read from the ``has_surr_charge`` column
By default, the value is read from the ``has_surr_charge`` column
in :func:`model_point`.
in :func:`model_point`.


.. seealso::
.. seealso::


* :func:`model_point`
* :func:`model_point`


"""
"""
return model_point()['has_surr_charge']
return model_point()['has_surr_charge'].values




def inflation_factor(t):
def inflation_factor(t):
"""The inflation factor at time t
"""The inflation factor at time t


.. seealso::
.. seealso::


* :func:`inflation_rate`
* :func:`inflation_rate`


"""
"""
return (1 + inflation_rate())**(t/12)
return (1 + inflation_rate())**(t/12)




def inflation_rate():
def inflation_rate():
"""Inflation rate
"""Inflation rate


The inflation rate to be applied to the expense assumption.
The inflation rate to be applied to the expense assumption.
By defualt it is set to ``0.01``.
By defualt it is set to ``0.01``.


.. seealso::
.. seealso::


* :func:`inflation_factor`
* :func:`inflation_factor`


"""
"""
return 0.01
return 0.01




def inv_income(t):
def inv_income(t):
"""Investment income on account value
"""Investment income on account value


Investment income earned on account value during each period.
Investment income earned on account value during each period.
For the plicies decreased by lapse and death, half
For the plicies decreased by lapse and death, half
the investment income is credited.
the investment income is credited.


.. seealso::
.. seealso::


* :func:`inv_income_pp`
* :func:`inv_income_pp`
* :func:`pols_if_at`
* :func:`pols_if_at`
* :func:`pols_death`
* :func:`pols_death`
* :func:`pols_lapse`
* :func:`pols_lapse`


"""
"""
return (inv_income_pp(t) * pols_if_at(t+1, "BEF_MAT")
return (inv_income_pp(t) * pols_if_at(t+1, "BEF_MAT")
+ 0.5 * inv_income_pp(t) * (pols_death(t) + pols_lapse(t)))
+ 0.5 * inv_income_pp(t) * (pols_death(t) + pols_lapse(t)))




def inv_income_pp(t):
def inv_income_pp(t):
"""Investment income on account value per policy
"""Investment income on account value per policy


Investment income on account value defined as::
Investment income on account value defined as::


inv_return_mth(t) * av_pp_at(t, "BEF_INV")
inv_return_mth(t) * av_pp_at(t, "BEF_INV")


.. seealso::
.. seealso::


* :func:`inv_return_mth`
* :func:`inv_return_mth`
* :func:`av_pp_at`
* :func:`av_pp_at`


"""
"""
return inv_return_mth(t) * av_pp_at(t, "BEF_INV")
return inv_return_mth(t) * av_pp_at(t, "BEF_INV")




def inv_return_mth(t):
def inv_return_mth(t):
"""Rate of investment return
"""Rate of investment return


Rate of monthly investment return for :attr:`scen_id` and ``t``
Rate of monthly investment return for :attr:`scen_id` and ``t``
read from :func:`inv_return_table`
read from :func:`inv_return_table`


.. seealso::
.. seealso::


* :func:`inv_return_table`
* :func:`inv_return_table`
* :attr:`scen_id`
* :attr:`scen_id`


"""
"""
return inv_return_table()[:, t]
return inv_return_table()[:, t]




def inv_return_table():
def inv_return_table():
r"""Table of investment return rates
r"""Table of investment return rates


Returns a Series of monthly investment retuns.
Returns a Series of monthly investment retuns.
The Series is indexed with ``scen_id`` and ``t`` which
The Series is indexed with ``scen_id`` and ``t`` which
is inh
is inherited from :attr:`std_norm_rand`.

.. math::

\exp\le