Finance and Economics Discussion Series (FEDS)
November 2024
Revisiting Risky Money
Abstract:
Risk was first incorporated into monetary aggregation over thirty-five years ago, using a stochastic version of the workhorse money-in-the-utility-function model. Nevertheless, the mathematical foundations of this stochastic model remain shaky. To firm the foundations, this paper employs a slightly richer probability concept than standard Borel-measurability, which enables me to prove the existence of a well-behaved solution and to derive stochastic Euler equations. This measurability approach is long-established albeit less common in economics, possibly because the derivation of stochastic Euler equations is new. Importantly, the problem’s economics are not restricted by the approach. Consequently, the results provide firm footing for the growing monetary aggregation under risk literature, which integrates monetary and finance theory. As crypto-currencies and stable coins garner more attention, solidifying the foundations of risky money becomes more critical. The method also supports deriving stochastic Euler equations for any dynamic economics problem that features contemporaneous uncertainty about prices, including asset pricing models like capm and stochastic consumer choice models.
Keywords: money; risk; monetary aggregation; asset pricing; dynamic programming; stochastic modeling; uncertainty; Euler equations
DOI: https://doi.org/10.17016/FEDS.2024.090
PDF: Full Paper
Disclaimer: The economic research that is linked from this page represents the views of the authors and does not indicate concurrence either by other members of the Board's staff or by the Board of Governors. The economic research and their conclusions are often preliminary and are circulated to stimulate discussion and critical comment. The Board values having a staff that conducts research on a wide range of economic topics and that explores a diverse array of perspectives on those topics. The resulting conversations in academia, the economic policy community, and the broader public are important to sharpening our collective thinking.