Working Paper

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 conceptthan standard Borel-measurability, which enables me to prove the existence of awell-behaved solution and to derive stochastic Euler equations. This measurabilityapproach 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;

JEL Classification: C61; C62; D81; D84; E40; G12;

https://doi.org/10.17016/FEDS.2024.090

Bibliographic Information

Provider: Board of Governors of the Federal Reserve System (U.S.)

Part of Series: Finance and Economics Discussion Series

Publication Date: 2024-11-26

Number: 2024-090