Optimal Control Study of Ethena's Yield-Bearing Stablecoin

This study formulates and solves a stochastic control problem for Ethena protocol's core yield strategy, which generates returns through a delta-neutral combination of long stETH positions and short ETH perpetual contracts of equal size. The model takes the rate of simultaneously buying stETH and shorting perpetual contracts as the control variable, incorporating both permanent price impact and temporary execution slippage. The study solves both the infinite-horizon discounted problem and the finite-horizon problem with terminal liquidation costs, obtaining explicit optimal control solutions in both cases.