Fiscal stimulus as an optimal control problem

Philip A. Ernst, Michael B. Imerman, Larry Shepp and Quan Zhou

Stochastic Processes and their Applications, 2022, vol. 150, issue C, 1091-1108

Abstract: During the Great Recession, Democrats in the United States argued that government spending could be utilized to “grease the wheels” of the economy in order to create wealth and to increase employment; Republicans, on the other hand, contended that government spending is wasteful and discourages investment, thereby increasing unemployment. This past year we have found ourselves in the midst of another crisis where government spending and fiscal stimulus is again being considered as a solution. In the present paper, we address this question by formulating an optimal control problem generalizing the model of Radner and Shepp (1996). The model allows for the company to borrow continuously from the government. We prove that there exists an optimal strategy; rigorous verification proofs for its optimality are provided. We proceed to prove that government loans increase the expected value of a company. We also examine the consequences of different profit-taking behaviors among firms who receive fiscal stimulus.

Keywords: Dividend problem; Radner–Shepp model; Fiscal stimulus; Financial strategy; Hamilton–Jacobi–Bellman equation; Stochastic control (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spa.2021.05.009

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