Trading under the proof‐of‐stake protocol – A continuous‐time control approach

We develop a continuous-time control approach to optimal trading in Proof-of-Stake (PoS) blockchain, formulated as consumption-investment problem that aims strike the balance between participant's (or agent's) utility from holding/trading stakes and consumption. present solutions via dynamic programming Hamilton-Jacobi-Bellman (HJB) equations. When functions are linear or convex, we derive close-form show bang-bang strategy is (i.e., always buy sell at full capacity). Furthermore, bring out explicit connection rate of return trading/holding risk-adjusted valuation stakes. In particular, when participant risk-neutral risk-seeking, corresponding being martingale sub-martingale, must be either all time, first then sell, with both buying selling executed capacity. also propose risk-control version problem; for special case, ''stake-parity'' problem, mean-reverting optimal.