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The Optimal Control of Government Stabilization Funds

Author

Listed:
  • Abel Cadenillas

    (Department of Mathematical and Statistical Sciences, University of Alberta, Central Academic Building 639, Edmonton, AB T6G 2G1, Canada)

  • Ricardo Huamán-Aguilar

    (Department of Economics, Pontificia Universidad Católica del Perú, Av. Universitaria 1801, San Miguel, Lima 32, Peru)

Abstract

We study the optimal control of a government stabilization fund, which is a mechanism to save money during good economic times to be used in bad economic times. The objective of the fund manager is to keep the fund as close as possible to a predetermined target. Accordingly, we consider a running cost associated with the difference between the actual fiscal fund and the fund target. The fund manager exerts control over the fund by making deposits in or withdrawals from the fund. The withdrawals are used to pay public debt or to finance government programs. We obtain, for the first time in the literature, the optimal band for the government stabilization fund. Our results are of interest to practitioners. For instance, we find that the higher the volatility, the larger the size of the optimal band. In particular, each country and state should have its own optimal fund band, in contrast to the “one-size-fits-all” approach that is often used in practice.

Suggested Citation

  • Abel Cadenillas & Ricardo Huamán-Aguilar, 2020. "The Optimal Control of Government Stabilization Funds," Mathematics, MDPI, vol. 8(11), pages 1-24, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:1975-:d:440903
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    References listed on IDEAS

    as
    1. J. Michael Harrison & Michael I. Taksar, 1983. "Instantaneous Control of Brownian Motion," Mathematics of Operations Research, INFORMS, vol. 8(3), pages 439-453, August.
    2. Abel Cadenillas & Sudipto Sarkar & Fernando Zapatero, 2007. "Optimal Dividend Policy With Mean‐Reverting Cash Reservoir," Mathematical Finance, Wiley Blackwell, vol. 17(1), pages 81-109, January.
    3. Giorgio Ferrari & Tiziano Vargiolu, 2020. "On the singular control of exchange rates," Annals of Operations Research, Springer, vol. 292(2), pages 795-832, September.
    4. Schwartz, Eduardo S, 1997. "The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging," Journal of Finance, American Finance Association, vol. 52(3), pages 923-973, July.
    5. Waud, Roger N, 1976. "Asymmetric Policymaker Utility Functions and Optimal Policy Under Uncertainty," Econometrica, Econometric Society, vol. 44(1), pages 53-66, January.
    6. Abel Cadenillas & Peter Lakner & Michael Pinedo, 2010. "Optimal Control of a Mean-Reverting Inventory," Operations Research, INFORMS, vol. 58(6), pages 1697-1710, December.
    7. Cristina Raluca Gh. Popescu & Gheorghe N. Popescu, 2019. "An Exploratory Study Based on a Questionnaire Concerning Green and Sustainable Finance, Corporate Social Responsibility, and Performance: Evidence from the Romanian Business Environment," JRFM, MDPI, vol. 12(4), pages 1-79, October.
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