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A Model for the Optimal Management of Inflation

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  • Salvatore Federico
  • Giorgio Ferrari
  • Patrick Schuhmann

Abstract

Consider a central bank that can adjust the inflation rate by increasing and decreasing the level of the key interest rate. Each intervention gives rise to proportional costs, and the central bank faces also a running penalty, e.g., due to misaligned levels of inflation and interest rate. We model the resulting minimization problem as a Markovian degenerate two-dimensional bounded-variation stochastic control problem. Its characteristic is that the mean-reversion level of the diffusive inflation rate is an affine function of the purely controlled interest rate's current value. By relying on a combination of techniques from viscosity theory and free-boundary analysis, we provide the structure of the value function and we show that it satisfies a second-order smooth-fit principle. Such a regularity is then exploited in order to determine a system of functional equations solved by the two monotone curves that split the control problem's state space in three connected regions.

Suggested Citation

  • Salvatore Federico & Giorgio Ferrari & Patrick Schuhmann, 2019. "A Model for the Optimal Management of Inflation," Department of Economics University of Siena 812, Department of Economics, University of Siena.
    • Handle: RePEc:usi:wpaper:812
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    File URL: http://repec.deps.unisi.it/quaderni/812.pdf
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    References listed on IDEAS

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    1. M. I. Taksar, 1985. "Average Optimal Singular Control and a Related Stopping Problem," Mathematics of Operations Research, INFORMS, vol. 10(1), pages 63-81, February.
    2. Pierre, Erwan & Villeneuve, Stéphane & Warin, Xavier, 2014. "Liquidity Management with Decreasing-returns-to-scale and Secured Credit Line," TSE Working Papers 14-542, Toulouse School of Economics (TSE), revised Jun 2016.
    3. Alvarez, Luis H. R., 2000. "Singular stochastic control in the presence of a state-dependent yield structure," Stochastic Processes and their Applications, Elsevier, vol. 86(2), pages 323-343, April.
    4. Erwan Pierre & Stéphane Villeneuve & Xavier Warin, 2016. "Liquidity management with decreasing returns to scale and secured credit line," Post-Print halshs-01522513, HAL.
    5. Tiziano De Angelis & Giorgio Ferrari & John Moriarty, 2014. "A Non Convex Singular Stochastic Control Problem and its Related Optimal Stopping Boundaries," Papers 1405.2442, arXiv.org, revised Nov 2014.
    6. Pui Chan Lon & Mihail Zervos, 2011. "A Model for Optimally Advertising and Launching a Product," Mathematics of Operations Research, INFORMS, vol. 36(2), pages 363-376, May.
    7. Erwan Pierre & Stéphane Villeneuve & Xavier Warin, 2016. "Liquidity management with decreasing returns to scale and secured credit line," Finance and Stochastics, Springer, vol. 20(4), pages 809-854, October.
    8. Tiziano De Angelis & Giorgio Ferrari & John Moriarty, 2019. "A Solvable Two-Dimensional Degenerate Singular Stochastic Control Problem with Nonconvex Costs," Mathematics of Operations Research, INFORMS, vol. 44(2), pages 512-531, May.
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    Cited by:

    1. Torben Koch & Tiziano Vargiolu, 2019. "Optimal Installation of Solar Panels with Price Impact: a Solvable Singular Stochastic Control Problem," Papers 1911.04223, arXiv.org.

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    More about this item

    Keywords

    singular stochastic control; Dynkin game; viscosity solution; free boundary; smooth-fit; inflation rate; interest rate; central bank policies;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • E58 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Central Banks and Their Policies

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