<reponame>footings/footings-actuarial<gh_stars>0
import functools
import operator
from typing import Optional, Union

import numpy as np
import pandas as pd


def calc_continuance(
    *decrements: pd.Series, starting_duration: Optional[pd.Series] = None,
) -> pd.Series:
    """Calculate continuance given a set of decrements.

    Parameters
    ----------
    *decrements : pd.Series
        The series of decrements to apply to calculate continuance.
    starting_duration : pd.Series, optional
        The start duration continuance value.

    Returns
    -------
    pd.Series
        The continuance table.

    Examples
    --------
    >>> import pandas as pd
    >>> from long_duration_mdk import calc_continuance
    >>> mortality_rate = pd.Series([0.01, 0.015, 0.02])
    >>> lapse_rate = pd.Series([0.2, 0.1, 0.05])

    Assume -
    - mortality is applied uniformly over a duration
    - lapse occurs only at end of duration

    Calculate continuance at the end of a duration.
    >>> lives_ed = calc_continuance(mortality_rate, lapse_rate)
    >>> lives_ed
    0   0.792000
    1   0.702108
    2   0.653663

    Shift one place to get the beginning duration value.
    >>> lives_bd = lives_ed.shift(1, fill_value=1)
    >>> lives_bd
    0   1.000000
    1   0.792000
    2   0.702108

    To get the value for the mid-point of the duration set a starting_duration value.
    >>> lives_md = calc_continuance(mortality_rate / 2, starting_duration=lives_bd)
    >>> lives_md
    0   0.995000
    1   0.786060
    2   0.695087
    """
    if starting_duration is None:
        return functools.reduce(operator.mul, [1 - d for d in decrements]).cumprod()
    return starting_duration * functools.reduce(operator.mul, [1 - d for d in decrements])


def calc_discount(
    interest_rate: pd.Series, *, t_adj: Optional[Union[int, float]] = None
) -> pd.Series:
    """Calculate the discount factor over a series.

    Parameters
    ----------
    interest_rate : pd.Series
        A series of interest rate values
    t_adj : Union[int, float], optional
        An optinal adjustment to the timing for the current duration. As an example, use 0.5 for a midpoint.

    Returns
    -------
    pd.Series
        The discount factor.

    Examples
    --------
    >>> import pandas as pd
    >>> from long_duration_mdk import calc_discount
    >>> interest_rate = pd.Series([0.03, 0.04, 0.05])
    >>> v_ed = calc_discount(interest_rate)
    >>> v_ed
    0    0.970874
    1    0.933532
    2    0.889079

    >>> v_md = calc_discount(interest_rate, t_adj=0.5)
    >>> v_md
    0    0.985329
    1    0.952020
    2    0.911034

    >>> v_bd = calc_discount(interest_rate, t_adj=0)
    >>> v_bd
    0    1.000000
    1    0.970874
    2    0.933532
    """
    cum = (1 + interest_rate).cumprod()
    if t_adj is not None:
        cum = cum.shift(1, fill_value=1) * (1 + interest_rate) ** t_adj
    return 1 / cum


def calc_interpolation(
    val_0: pd.Series,
    val_1: pd.Series,
    wt_0: pd.Series,
    wt_1: Optional[pd.Series] = None,
    method: str = "linear",
) -> pd.Series:
    """Calculate interpolation between two values.

    Parameters
    ----------
    val_0 : pd.Series
        zzz
    val_1 : pd.Sereis
        zzz
    wt_0 : pd.Series
        zzz
    wt_1 : pd.Series, optional
        zzz
    method : str
        zzz

    Returns
    -------
    pd.Series
        The interpolated values.

    Examples
    --------
    >>> import pandas as pd
    >>> from long_duration_mdk import calc_interpolation
    >>> val_0 = pd.Series([1, 2, 3])
    >>> val_1 = pd.Series([2, 3, 4])
    >>> wt_0 = pd.Series([0.5, 0.5, 0.5])
    >>> linear = calc_interpolation(val_0, val_1, wt_0, method="linear")
    >>> linear
    0    1.5
    1    2.5
    2    3.5
    >>> log = calc_interpolation(val_0, val_1, wt_0, method="log-linear")
    >>> log
    0    1.414214
    1    2.449490
    2    3.464102
    """
    if wt_1 is None:
        wt_1 = 1 - wt_0
    if method == "linear":
        ret = val_0 * wt_0 + val_1 * wt_1
    elif method == "log-linear":
        if val_0.min() < 0 or val_1.min() < 0:
            msg = f"No values in val_0 (min = {val_0.min()}) or "
            msg += f"val_1 (min = {val_1.min()}) can be less than 0."
            raise ValueError(msg)
        elif val_0.min() == 0 or val_1.min() == 0:
            val_0 = np.log(val_0 + 1)
            val_1 = np.log(val_1 + 1)
            ret = pd.Series(np.exp(val_0 * wt_0 + val_1 * wt_1)) - 1
        else:
            val_0 = np.log(val_0)
            val_1 = np.log(val_1)
            ret = pd.Series(np.exp(val_0 * wt_0 + val_1 * wt_1))
    else:
        msg = f"The value passed to method [{str(method)}] is not recognized."
        msg += " Please use one of 'linear' or 'log'."
        raise ValueError(msg)

    return ret


def calc_pv(series: pd.Series) -> pd.Series:
    """Calculate the present value of a series.

    Parameters
    ----------
    series : pd.Series
        The series to calculate the present value from.

    Returns
    -------
    pd.Series
        The series with the present value for each row.

    Examples
    --------
    >>> import pandas as pd
    >>> from long_duration_mdk import calc_pv
    >>> x = calc_pv(pd.Series([3, 2, 1]))
    0    6
    1    3
    2    1
    """
    return series[::-1].cumsum()[::-1]


def calc_pvfnb(pvfb: pd.Series, pvfp: pd.Series, net_benefit_method: str) -> pd.Series:
    """Calculate the present value of net future benefits.

    Parameters
    ----------
    pvfb : pd.Series
        A series representing the present value of future benefits.
    pvfp : pd.Series
        A series representing the present value of premium future premium.
    net_benefit_method : str
        The net benefit method to use. Set to  -
        - NLP for net level premium
        - PT1 for 1 year preliminary term
        - PT2 for 2 year preliminary term

    Returns
    -------
    pd.Series
        A series representing the present value of net future benefits.

    Examples
    --------
    >>> import pandas as pd
    >>> from long_duration_mdk import calc_pvfnb
    >>> pvfb = pd.Series([6, 5, 3])
    >>> pvfp = pd.Series([9, 6, 3])
    >>> pvfnb = calc_pvfnb(pvfb=pvfb, pvfp=pvfp, net_benefit_method="NLP")
    >>> pvfnb
    0    6.0
    1    4.0
    2    2.0
    """
    if net_benefit_method == "NLP":
        nlp = pvfb.iat[0] / pvfp.iat[0]
        pvfnb = pvfp * nlp
    elif net_benefit_method == "PT1":
        nlp = pvfb.iat[1] / pvfp.iat[1]
        pvfnb = pvfp * nlp
        pvfnb.iat[0] = pvfb.iat[0]
    elif net_benefit_method == "PT2":
        nlp = pvfb.iat[2] / pvfp.iat[2]
        pvfnb = pvfp * nlp
        pvfnb.iat[0] = pvfb.iat[0]
        pvfnb.iat[1] = pvfb.iat[1]
    else:
        msg = f"The net_benefit_method of [{net_benefit_method}] is not recognized."
        msg += " Use one of NLP, PT1, or PT2."
        raise ValueError(msg)
    return pvfnb


def calc_benefit_reserve(
    pvfb: pd.Series, pvfnb: pd.Series, lives: pd.Series, discount: pd.Series,
) -> pd.Series:
    """Calculate benefit reserve.

    Parameters
    ----------
    pvfb : pd.Series
        A series representing the present value of future benefits.
    pvfnb : pd.Series
        A series representing the present value of future net benefits.
    lives : pd.Series
        A series representing the expected lives inforce.
    discount : pd.Series
        A series representing the discount factor.

    Returns
    -------
    pd.Series
        The benefit reserve over time.

    Examples
    --------
    >>> import pandas as pd
    >>> from long_duration_mdk import calc_pvfnb, calc_benefit_reserve
    >>> pvfb = pd.Series([6, 5, 3])
    >>> pvfp = pd.Series([9, 6, 3])
    >>> pvfnb = calc_pvfnb(pvfb=pvfb, pvfp=pvfp, net_benefit_method="NLP")
    >>> lives = pd.Series([0.95, 0.9, 0.8])
    >>> discount = pd.Series([0.95, 0.9, 0.85])
    >>> calc_benefit_reserve(
    ...     pvfb=pvfb,
    ...     pvfnb=pvfnb,
    ...     lives=lives,
    ...     discount=discount,
    ... )
    0    1.108033
    1    1.234568
    2    0.000000
    """
    return (pvfb - pvfnb).shift(-1, fill_value=0) / lives / discount


# def calc_change_in_reserve(
#     reserve: pd.Series, lives: pd.Series, discount: pd.Series
# ):
#     """Calculate change in reserve."""
#     discount_shift = discount.shift(1, fill_value=1)
#     current_period = reserve * lives / (discount_shift / discount)
#     prior_period = reserve.shift(1, fill_value=0) * lives.shift(1, fill_value=1)
#     return current_period - prior_period


# def calc_policy_year_benefit_reserve(
#     gross_premiums: pd.Series,
#     benefits: pd.Series,
#     lives: pd.Series,
#     discount: pd.Series,
#     net_benefit_method: str,
# ):
#     """Calculate a policy year benefit reserve.
#
#     Parameters
#     ----------
#     gross_premiums : pd.Series
#         The projected stream  of gross premiums.
#     benefits : pd.Series
#         The projected stream of benefits.
#     lives : pd.Series
#         The projected lives inforce at each duration.
#     discount : pd.Series
#         The discount to apply.
#     net_benefit_method : str
#         The net benefit method to use. Options are -
#             - NLP (Net Level Premium)
#             - PT1 (1 Year Preliminary Term)
#             - PT2 (2 Year Preliminary Term)
#
#     Returns
#     -------
#     pd.Series
#         A series with the benefit reserves.
#     """
#     pvfb = calc_pv(benefits * lives * discount)
#     pvp = calc_pv(gross_premiums * lives * discount)
#     pvfnb = calc_pvfnb(pvfb, pvp, net_benefit_method)
#     benefit_reserve = (pvfb - pvfnb) / discount
#     return benefit_reserve

import functools
import operator
from typing import Optional, Union

import numpy as np
import pandas as pd


def calc_continuance(
    *decrements: pd.Series, starting_duration: Optional[pd.Series] = None,
) -> pd.Series:
    """Calculate continuance given a set of decrements.

    Parameters
    ----------
    *decrements : pd.Series
        The series of decrements to apply to calculate continuance.
    starting_duration : pd.Series, optional
        The start duration continuance value.

    Returns
    -------
    pd.Series
        The continuance table.

    Examples
    --------
    >>> import pandas as pd
    >>> from long_duration_mdk import calc_continuance
    >>> mortality_rate = pd.Series([0.01, 0.015, 0.02])
    >>> lapse_rate = pd.Series([0.2, 0.1, 0.05])

    Assume -
    - mortality is applied uniformly over a duration
    - lapse occurs only at end of duration

    Calculate continuance at the end of a duration.
    >>> lives_ed = calc_continuance(mortality_rate, lapse_rate)
    >>> lives_ed
    0   0.792000
    1   0.702108
    2   0.653663

    Shift one place to get the beginning duration value.
    >>> lives_bd = lives_ed.shift(1, fill_value=1)
    >>> lives_bd
    0   1.000000
    1   0.792000
    2   0.702108

    To get the value for the mid-point of the duration set a starting_duration value.
    >>> lives_md = calc_continuance(mortality_rate / 2, starting_duration=lives_bd)
    >>> lives_md
    0   0.995000
    1   0.786060
    2   0.695087
    """
    if starting_duration is None:
        return functools.reduce(operator.mul, [1 - d for d in decrements]).cumprod()
    return starting_duration * functools.reduce(operator.mul, [1 - d for d in decrements])


def calc_discount(
    interest_rate: pd.Series, *, t_adj: Optional[Union[int, float]] = None
) -> pd.Series:
    """Calculate the discount factor over a series.

    Parameters
    ----------
    interest_rate : pd.Series
        A series of interest rate values
    t_adj : Union[int, float], optional
        An optinal adjustment to the timing for the current duration. As an example, use 0.5 for a midpoint.

    Returns
    -------
    pd.Series
        The discount factor.

    Examples
    --------
    >>> import pandas as pd
    >>> from long_duration_mdk import calc_discount
    >>> interest_rate = pd.Series([0.03, 0.04, 0.05])
    >>> v_ed = calc_discount(interest_rate)
    >>> v_ed
    0    0.970874
    1    0.933532
    2    0.889079

    >>> v_md = calc_discount(interest_rate, t_adj=0.5)
    >>> v_md
    0    0.985329
    1    0.952020
    2    0.911034

    >>> v_bd = calc_discount(interest_rate, t_adj=0)
    >>> v_bd
    0    1.000000
    1    0.970874
    2    0.933532
    """
    cum = (1 + interest_rate).cumprod()
    if t_adj is not None:
        cum = cum.shift(1, fill_value=1) * (1 + interest_rate) ** t_adj
    return 1 / cum


def calc_interpolation(
    val_0: pd.Series,
    val_1: pd.Series,
    wt_0: pd.Series,
    wt_1: Optional[pd.Series] = None,
    method: str = "linear",
) -> pd.Series:
    """Calculate interpolation between two values.

    Parameters
    ----------
    val_0 : pd.Series
        zzz
    val_1 : pd.Sereis
        zzz
    wt_0 : pd.Series
        zzz
    wt_1 : pd.Series, optional
        zzz
    method : str
        zzz

    Returns
    -------
    pd.Series
        The interpolated values.

    Examples
    --------
    >>> import pandas as pd
    >>> from long_duration_mdk import calc_interpolation
    >>> val_0 = pd.Series([1, 2, 3])
    >>> val_1 = pd.Series([2, 3, 4])
    >>> wt_0 = pd.Series([0.5, 0.5, 0.5])
    >>> linear = calc_interpolation(val_0, val_1, wt_0, method="linear")
    >>> linear
    0    1.5
    1    2.5
    2    3.5
    >>> log = calc_interpolation(val_0, val_1, wt_0, method="log-linear")
    >>> log
    0    1.414214
    1    2.449490
    2    3.464102
    """
    if wt_1 is None:
        wt_1 = 1 - wt_0
    if method == "linear":
        ret = val_0 * wt_0 + val_1 * wt_1
    elif method == "log-linear":
        if val_0.min() < 0 or val_1.min() < 0:
            msg = f"No values in val_0 (min = {val_0.min()}) or "
            msg += f"val_1 (min = {val_1.min()}) can be less than 0."
            raise ValueError(msg)
        elif val_0.min() == 0 or val_1.min() == 0:
            val_0 = np.log(val_0 + 1)
            val_1 = np.log(val_1 + 1)
            ret = pd.Series(np.exp(val_0 * wt_0 + val_1 * wt_1)) - 1
        else:
            val_0 = np.log(val_0)
            val_1 = np.log(val_1)
            ret = pd.Series(np.exp(val_0 * wt_0 + val_1 * wt_1))
    else:
        msg = f"The value passed to method [{str(method)}] is not recognized."
        msg += " Please use one of 'linear' or 'log'."
        raise ValueError(msg)

    return ret


def calc_pv(series: pd.Series) -> pd.Series:
    """Calculate the present value of a series.

    Parameters
    ----------
    series : pd.Series
        The series to calculate the present value from.

    Returns
    -------
    pd.Series
        The series with the present value for each row.

    Examples
    --------
    >>> import pandas as pd
    >>> from long_duration_mdk import calc_pv
    >>> x = calc_pv(pd.Series([3, 2, 1]))
    0    6
    1    3
    2    1
    """
    return series[::-1].cumsum()[::-1]


def calc_pvfnb(pvfb: pd.Series, pvfp: pd.Series, net_benefit_method: str) -> pd.Series:
    """Calculate the present value of net future benefits.

    Parameters
    ----------
    pvfb : pd.Series
        A series representing the present value of future benefits.
    pvfp : pd.Series
        A series representing the present value of premium future premium.
    net_benefit_method : str
        The net benefit method to use. Set to  -
        - NLP for net level premium
        - PT1 for 1 year preliminary term
        - PT2 for 2 year preliminary term

    Returns
    -------
    pd.Series
        A series representing the present value of net future benefits.

    Examples
    --------
    >>> import pandas as pd
    >>> from long_duration_mdk import calc_pvfnb
    >>> pvfb = pd.Series([6, 5, 3])
    >>> pvfp = pd.Series([9, 6, 3])
    >>> pvfnb = calc_pvfnb(pvfb=pvfb, pvfp=pvfp, net_benefit_method="NLP")
    >>> pvfnb
    0    6.0
    1    4.0
    2    2.0
    """
    if net_benefit_method == "NLP":
        nlp = pvfb.iat[0] / pvfp.iat[0]
        pvfnb = pvfp * nlp
    elif net_benefit_method == "PT1":
        nlp = pvfb.iat[1] / pvfp.iat[1]
        pvfnb = pvfp * nlp
        pvfnb.iat[0] = pvfb.iat[0]
    elif net_benefit_method == "PT2":
        nlp = pvfb.iat[2] / pvfp.iat[2]
        pvfnb = pvfp * nlp
        pvfnb.iat[0] = pvfb.iat[0]
        pvfnb.iat[1] = pvfb.iat[1]
    else:
        msg = f"The net_benefit_method of [{net_benefit_method}] is not recognized."
        msg += " Use one of NLP, PT1, or PT2."
        raise ValueError(msg)
    return pvfnb


def calc_benefit_reserve(
    pvfb: pd.Series, pvfnb: pd.Series, lives: pd.Series, discount: pd.Series,
) -> pd.Series:
    """Calculate benefit reserve.

    Parameters
    ----------
    pvfb : pd.Series
        A series representing the present value of future benefits.
    pvfnb : pd.Series
        A series representing the present value of future net benefits.
    lives : pd.Series
        A series representing the expected lives inforce.
    discount : pd.Series
        A series representing the discount factor.

    Returns
    -------
    pd.Series
        The benefit reserve over time.

    Examples
    --------
    >>> import pandas as pd
    >>> from long_duration_mdk import calc_pvfnb, calc_benefit_reserve
    >>> pvfb = pd.Series([6, 5, 3])
    >>> pvfp = pd.Series([9, 6, 3])
    >>> pvfnb = calc_pvfnb(pvfb=pvfb, pvfp=pvfp, net_benefit_method="NLP")
    >>> lives = pd.Series([0.95, 0.9, 0.8])
    >>> discount = pd.Series([0.95, 0.9, 0.85])
    >>> calc_benefit_reserve(
    ...     pvfb=pvfb,
    ...     pvfnb=pvfnb,
    ...     lives=lives,
    ...     discount=discount,
    ... )
    0    1.108033
    1    1.234568
    2    0.000000
    """
    return (pvfb - pvfnb).shift(-1, fill_value=0) / lives / discount


# def calc_change_in_reserve(
#     reserve: pd.Series, lives: pd.Series, discount: pd.Series
# ):
#     """Calculate change in reserve."""
#     discount_shift = discount.shift(1, fill_value=1)
#     current_period = reserve * lives / (discount_shift / discount)
#     prior_period = reserve.shift(1, fill_value=0) * lives.shift(1, fill_value=1)
#     return current_period - prior_period


# def calc_policy_year_benefit_reserve(
#     gross_premiums: pd.Series,
#     benefits: pd.Series,
#     lives: pd.Series,
#     discount: pd.Series,
#     net_benefit_method: str,
# ):
#     """Calculate a policy year benefit reserve.
#
#     Parameters
#     ----------
#     gross_premiums : pd.Series
#         The projected stream  of gross premiums.
#     benefits : pd.Series
#         The projected stream of benefits.
#     lives : pd.Series
#         The projected lives inforce at each duration.
#     discount : pd.Series
#         The discount to apply.
#     net_benefit_method : str
#         The net benefit method to use. Options are -
#             - NLP (Net Level Premium)
#             - PT1 (1 Year Preliminary Term)
#             - PT2 (2 Year Preliminary Term)
#
#     Returns
#     -------
#     pd.Series
#         A series with the benefit reserves.
#     """
#     pvfb = calc_pv(benefits * lives * discount)
#     pvp = calc_pv(gross_premiums * lives * discount)
#     pvfnb = calc_pvfnb(pvfb, pvp, net_benefit_method)
#     benefit_reserve = (pvfb - pvfnb) / discount
#     return benefit_reserve
Calculate continuance given a set of decrements.      Parameters     ----------     *decrements : pd.Series         The series of decrements to apply to calculate continuance.     starting_duration : pd.Series, optional         The start duration continuance value.      Returns     -------     pd.Series         The continuance table.      Examples     --------     >>> import pandas as pd     >>> from long_duration_mdk import calc_continuance     >>> mortality_rate = pd.Series([0.01, 0.015, 0.02])     >>> lapse_rate = pd.Series([0.2, 0.1, 0.05])      Assume -     - mortality is applied uniformly over a duration     - lapse occurs only at end of duration      Calculate continuance at the end of a duration.     >>> lives_ed = calc_continuance(mortality_rate, lapse_rate)     >>> lives_ed     0   0.792000     1   0.702108     2   0.653663      Shift one place to get the beginning duration value.     >>> lives_bd = lives_ed.shift(1, fill_value=1)     >>> lives_bd     0   1.000000     1   0.792000     2   0.702108      To get the value for the mid-point of the duration set a starting_duration value.     >>> lives_md = calc_continuance(mortality_rate / 2, starting_duration=lives_bd)     >>> lives_md     0   0.995000     1   0.786060     2   0.695087 Calculate the discount factor over a series.      Parameters     ----------     interest_rate : pd.Series         A series of interest rate values     t_adj : Union[int, float], optional         An optinal adjustment to the timing for the current duration. As an example, use 0.5 for a midpoint.      Returns     -------     pd.Series         The discount factor.      Examples     --------     >>> import pandas as pd     >>> from long_duration_mdk import calc_discount     >>> interest_rate = pd.Series([0.03, 0.04, 0.05])     >>> v_ed = calc_discount(interest_rate)     >>> v_ed     0    0.970874     1    0.933532     2    0.889079      >>> v_md = calc_discount(interest_rate, t_adj=0.5)     >>> v_md     0    0.985329     1    0.952020     2    0.911034      >>> v_bd = calc_discount(interest_rate, t_adj=0)     >>> v_bd     0    1.000000     1    0.970874     2    0.933532 Calculate interpolation between two values.      Parameters     ----------     val_0 : pd.Series         zzz     val_1 : pd.Sereis         zzz     wt_0 : pd.Series         zzz     wt_1 : pd.Series, optional         zzz     method : str         zzz      Returns     -------     pd.Series         The interpolated values.      Examples     --------     >>> import pandas as pd     >>> from long_duration_mdk import calc_interpolation     >>> val_0 = pd.Series([1, 2, 3])     >>> val_1 = pd.Series([2, 3, 4])     >>> wt_0 = pd.Series([0.5, 0.5, 0.5])     >>> linear = calc_interpolation(val_0, val_1, wt_0, method="linear")     >>> linear     0    1.5     1    2.5     2    3.5     >>> log = calc_interpolation(val_0, val_1, wt_0, method="log-linear")     >>> log     0    1.414214     1    2.449490     2    3.464102 Calculate the present value of a series.      Parameters     ----------     series : pd.Series         The series to calculate the present value from.      Returns     -------     pd.Series         The series with the present value for each row.      Examples     --------     >>> import pandas as pd     >>> from long_duration_mdk import calc_pv     >>> x = calc_pv(pd.Series([3, 2, 1]))     0    6     1    3     2    1 Calculate the present value of net future benefits.      Parameters     ----------     pvfb : pd.Series         A series representing the present value of future benefits.     pvfp : pd.Series         A series representing the present value of premium future premium.     net_benefit_method : str         The net benefit method to use. Set to  -         - NLP for net level premium         - PT1 for 1 year preliminary term         - PT2 for 2 year preliminary term      Returns     -------     pd.Series         A series representing the present value of net future benefits.      Examples     --------     >>> import pandas as pd     >>> from long_duration_mdk import calc_pvfnb     >>> pvfb = pd.Series([6, 5, 3])     >>> pvfp = pd.Series([9, 6, 3])     >>> pvfnb = calc_pvfnb(pvfb=pvfb, pvfp=pvfp, net_benefit_method="NLP")     >>> pvfnb     0    6.0     1    4.0     2    2.0 Calculate benefit reserve.      Parameters     ----------     pvfb : pd.Series         A series representing the present value of future benefits.     pvfnb : pd.Series         A series representing the present value of future net benefits.     lives : pd.Series         A series representing the expected lives inforce.     discount : pd.Series         A series representing the discount factor.      Returns     -------     pd.Series         The benefit reserve over time.      Examples     --------     >>> import pandas as pd     >>> from long_duration_mdk import calc_pvfnb, calc_benefit_reserve     >>> pvfb = pd.Series([6, 5, 3])     >>> pvfp = pd.Series([9, 6, 3])     >>> pvfnb = calc_pvfnb(pvfb=pvfb, pvfp=pvfp, net_benefit_method="NLP")     >>> lives = pd.Series([0.95, 0.9, 0.8])     >>> discount = pd.Series([0.95, 0.9, 0.85])     >>> calc_benefit_reserve(     ...     pvfb=pvfb,     ...     pvfnb=pvfnb,     ...     lives=lives,     ...     discount=discount,     ... )     0    1.108033     1    1.234568     2    0.000000 # def calc_change_in_reserve( #     reserve: pd.Series, lives: pd.Series, discount: pd.Series # ): #     """Calculate change in reserve.""" #     discount_shift = discount.shift(1, fill_value=1) #     current_period = reserve * lives / (discount_shift / discount) #     prior_period = reserve.shift(1, fill_value=0) * lives.shift(1, fill_value=1) #     return current_period - prior_period # def calc_policy_year_benefit_reserve( #     gross_premiums: pd.Series, #     benefits: pd.Series, #     lives: pd.Series, #     discount: pd.Series, #     net_benefit_method: str, # ): #     """Calculate a policy year benefit reserve. # #     Parameters #     ---------- #     gross_premiums : pd.Series #         The projected stream  of gross premiums. #     benefits : pd.Series #         The projected stream of benefits. #     lives : pd.Series #         The projected lives inforce at each duration. #     discount : pd.Series #         The discount to apply. #     net_benefit_method : str #         The net benefit method to use. Options are - #             - NLP (Net Level Premium) #             - PT1 (1 Year Preliminary Term) #             - PT2 (2 Year Preliminary Term) # #     Returns #     ------- #     pd.Series #         A series with the benefit reserves. #     """ #     pvfb = calc_pv(benefits * lives * discount) #     pvp = calc_pv(gross_premiums * lives * discount) #     pvfnb = calc_pvfnb(pvfb, pvp, net_benefit_method) #     benefit_reserve = (pvfb - pvfnb) / discount #     return benefit_reserve