Optimal Control of Reserve Asset Portfolios for Pegged Digital Currencies

Abstract: Stablecoins promise par convertibility, yet issuers must balance immediate liquidity against yield on reserves to keep the peg credible. We study this treasury problem as a continuous-time control task with two instruments: reallocating reserves between cash and short-duration government bills, and setting a spread fee for either minting or burning the coin. Mint and redemption flows follow mutually exciting processes that reproduce clustered order flow; peg deviations arise when redemptions exceed liquid reserves within settlement windows. We develop a stochastic model predictive control framework that incorporates moment closure for event intensities. Using Pontryagin's Maximum Principle, we demonstrate that the optimal control exhibits a bang-off-bang structure: each asset type is purchased at maximum capacity when the utility difference exceeds the corresponding difference in shadow costs. Introducing settlement windows leads to a sampled-data implementation with a simple threshold (soft-thresholding) structure for rebalancing. We also establish a monotone stress-response property: as expected outflows intensify or windows lengthen, the optimal policy shifts predictably toward cash. In simulations covering various stress test scenarios, the controller preserves most bill carry in calm markets, builds cash quickly when stress emerges, and avoids unnecessary rotations under transitory signals. The proposed policy is implementation-ready and aligns naturally with operational cut-offs. Our results translate empirical flow risk into auditable treasury rules that improve peg quality without sacrificing avoidable carry.