Optimal Control of Reserve Asset Portfolios for Stablecoins

TL;DR

This paper develops a stochastic control framework for stablecoin reserves, balancing liquidity and yield through reallocation and fee-setting, to maintain peg stability amid clustered order flows and market stress.

Contribution

It introduces a novel control model incorporating moment closure and soft-thresholding for reserve management, providing a practical, implementable policy for stablecoin peg stability.

Findings

Optimal reallocation exhibits a soft-thresholding structure.

Controller maintains peg stability under stress scenarios.

Policy aligns with operational cut-offs and improves peg quality.

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 immediate cash coverage is insufficient relative to outstanding supply, and the market price relaxes toward this liquidity-coverage fair value. We develop a stochastic model predictive control framework that incorporates moment closure for event intensities. Using Pontryagin's Maximum Principle, we show that the optimal reallocation control exhibits a soft-thresholding structure: no rebalancing occurs when the shadow-cost differential lies within a deadzone set by transaction costs, and reallocation scales linearly beyond that threshold up to a capacity-imposed saturation limit. 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.