Trading under the proof‐of‐stake protocol – A continuous‐time control approach
Trading under the proof‐of‐stake protocol – A continuous‐time control approach
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DOI：
10.1111/mafi.12403
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发表时间：
2022-07
影响因子：
1.6
通讯作者：
Wenpin Tang;D. Yao
中科院分区：
文献类型：
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作者：
Wenpin Tang;D. Yao
我们开发了一种连续时间控制方法来实现权益证明（PoS）区块链中的最优交易，将其表述为消费投资问题，旨在在参与者（或代理人）持有/交易权益的效用和消费效用之间取得最佳平衡。我们通过动态规划和 Hamilton-Jacobi-Bellman (HJB) 方程提出解决方案。当效用函数为线性或凸函数时，我们得出封闭式解，并表明爆炸策略是最优的（即始终满负荷买入或卖出）。此外，我们还提出了交易/持有股权的回报率与参与者的风险调整后的股权估值之间的明确联系。特别是，我们表明，当参与者是风险中性或风险寻求时，对应于风险调整后的估值是鞅或子鞅，最优策略必须是要么一直买入，一直卖出，或者先买入然后卖出，并且买入和卖出都满负荷执行。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，即“权益平价”问题，我们证明均值回归策略是最优的。
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.