Stochastic Dedication model with borrowing and lending variables

StochDedicationBL.py StochDedicationBL.gdx

"""
## GAMSSOURCE: https://www.gams.com/latest/finlib_ml/libhtml/finlib_StochDedicationBL.html
## LICENSETYPE: Community
## MODELTYPE: LP
## DATAFILES: StochDedicationBL.gdx


Stochastic Dedication model with borrowing and lending variables

* StochDedicationBL.gms: Stochastic Dedication model with borrowing
* and lending variables.
* Consiglio, Nielsen and Zenios.
* PRACTICAL FINANCIAL OPTIMIZATION: A Library of GAMS Models, Section 6.2.2
* Last modified: Apr 2008.
"""

from __future__ import annotations

import os
from pathlib import Path

from gamspy import Container
from gamspy import Equation
from gamspy import Model
from gamspy import Sense
from gamspy import Sum
from gamspy import Variable


def main():
    # Define container
    m = Container(
        system_directory=os.getenv("SYSTEM_DIRECTORY", None),
        delayed_execution=int(os.getenv("DELAYED_EXECUTION", False)),
        load_from=str(Path(__file__).parent.absolute())
        + "/StochDedicationBL.gdx",
    )

    # Aliases
    l, t = m.getSymbols(["l", "t"])

    # Scalars
    Horizon = m.getSymbols(["Horizon"])[0]

    # Parameters
    tau = m.getSymbols(["tau"])[0]

    # Aliases
    i = m.getSymbols(["i"])[0]

    # Scalars
    spread = m.getSymbols(["spread"])[0]

    # Parameters
    Price = m.getSymbols(["Price"])[0]

    # Parameters
    Srf, SF, SLiability = m.getSymbols([
        "Srf",
        "SF",
        "SLiability",
    ])

    # Variables
    x = Variable(
        m, "x", domain=i, type="Positive", description="Face value purchased"
    )
    surplus = Variable(
        m,
        "surplus",
        domain=[t, l],
        type="Positive",
        description="Amount of money reinvested",
    )
    borrow = Variable(
        m,
        "borrow",
        domain=[t, l],
        type="Positive",
        description="Amount of money borrowed",
    )
    v0 = Variable(m, "v0", description="Upfront investment")

    # Equations
    CashFlowCon = Equation(
        m,
        "CashFlowCon",
        domain=[t, l],
        description="Equations defining the cashflow balance",
    )

    CashFlowCon[t, l] = (
        Sum(i, SF[t, i, l] * x[i]).where[tau[t] > 0]
        + (v0 - Sum(i, Price[i] * x[i])).where[tau[t] == 0]
        + ((1 + Srf[t.lag(1), l]) * surplus[t.lag(1), l]).where[tau[t] > 0]
        + borrow[t, l].where[tau[t] < Horizon]
        == surplus[t, l]
        + SLiability[t, l].where[tau[t] > 0]
        + ((1 + Srf[t.lag(1), l] + spread) * borrow[t.lag(1), l]).where[
            tau[t] > 0
        ]
    )

    StochDedicationBL = Model(
        m,
        name="StochDedicationBL",
        equations=[CashFlowCon],
        problem="LP",
        sense=Sense.MIN,
        objective=v0,
    )

    StochDedicationBL.solve()
    print("Objective Function Value: ", round(v0.records.level[0], 3))

    print(x.description, ": \n", x.records.loc[:, ["i", "level"]])


if __name__ == "__main__":
    main()