## A Martingale Approach to the Question of Fiscal Stimulus (Michael Imerman, CGU)

### December 3, 2018 @ 4:15 pm - 5:15 pm

*Joint work with Larry Shepp & Philip Ernst*

In this paper we develop a mathematical model to address an ongoing politico-economic debate between Democrats and Republicans. Democrats in the US say that government spending can be used to “grease the wheels’ of the economy, create wealth, and increase employment; the Republicans say that government spending is wasteful, discourages investment, and so increases unemployment. These arguments cannot both be correct, but both arguments seem meritorious. We address this economic question of fiscal stimulus as a new optimal control problem extending the model of Radner-Shepp (1996). A unique solution is found using traditional martingale methods for stochastic optimization along with a numerical procedure to solve a non-homogeneous ODE as the root of an implicit function. Specifically, we find that there exists an optimal strategy with interesting mathematical properties.