The challenges of fiscal sustainability are often faced by most governments in the period of expansionary policies. As primary sources of fiscal revenue, tax and debt are essential for ensuring sustainable fiscal development and maintaining economic and financial stability. The question of how to effectively balance debt and tax to achieve fiscal sustainability for governments has thus become a critical area of study. Recognizing that the financial market is subject to Knightian uncertainty, this paper employs nonlinear expectation theory to develop a dynamic model of optimal government tax and debt. The model derives a Hamilton-Jacobi-Bellman (HJB) equation that governs household value and further examines the effects of Knightian uncertainty on household value, marginal cost of debt, optimal government tax rates, and the time to reach the government’s debt capacity. Numerical simulations of the theoretical results reveal that higher levels of Knightian uncertainty increase the marginal costs of both tax and debt, while shortening the duration to reach their debt capacity for the governments.
Fei et al. (2026) studied this question.