论文标题
在验证证明方案下进行交易 - 一种连续的时间控制方法
Trading under the Proof-of-Stake Protocol -- a Continuous-Time Control Approach
论文作者
论文摘要
我们开发了一种连续的时间控制方法，以在有验证验证（POS）区块链中进行最佳交易，该区块链被表达为一种消费式评估问题，旨在从参与者（或代理商）效用之间取得最佳平衡，从持有/交易赌注和消费中的公用事业中。我们通过动态编程和Hamilton-Jacobi-Bellman（HJB）方程提出解决方案。当实用程序功能是线性或凸功能时，我们会得出近距离的解决方案，并表明Bang-bang策略是最佳的（即，始终以全容量购买或出售）。此外，我们提出了交易/持有股份回报率与参与者对股份风险调整的估值之间的明确联系。特别是，我们表明参与者何时是风险中立或寻求风险的，对应于风险调整后的估值是Martingale或次级婚姻，最佳策略必须是一直以来一直在购买，始终出售，或者是首选，然后出售，然后出售以及以全额容量执行和销售。我们还提出了消费投资问题的风险控制版本；对于特殊情况，“股份 - 差异”问题，我们表明一种均值转移策略是最佳的。
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.
