Trading under the proof‐of‐stake protocol – A continuous‐time control approach
研究了权益证明区块链中的最优交易问题，通过连续时间控制方法求解消费-投资模型，发现线性或凸效用下最优策略是满仓买卖，并揭示了收益率与风险调整估值的关系。
Abstract We develop a continuous‐time control approach to optimal trading in a Proof‐of‐Stake (PoS) blockchain, formulated as a consumption‐investment problem that aims to strike the optimal balance between a participant's (or agent's) utility from holding/trading stakes and utility from consumption. We present solutions via dynamic programming and the Hamilton–Jacobi–Bellman (HJB) equations. When the utility functions are linear or convex, we derive close‐form solutions and show that the bang‐bang strategy is optimal (i.e., always buy or sell at full capacity). Furthermore, we bring out the explicit connection between the rate of return in trading/holding stakes and the participant's risk‐adjusted valuation of the stakes. In particular, we show when a participant is risk‐neutral or risk‐seeking, corresponding to the risk‐adjusted valuation being a martingale or a sub‐martingale, the optimal strategy must be to either buy all the time, sell all the time, or first buy then sell, and with both buying and selling executed at full capacity. We also propose a risk‐control version of the consumption‐investment problem; and for a special case, the “stake‐parity” problem, we show a mean‐reverting strategy is optimal.