Abstract: The shock of investors’ investment efficiency has an impact on platform productivity in platform operation, thus affecting the platform token issuance strategy, token price, and platform franchise value. Considering the Knightian uncertainty of investors’ investment efficiency impact, a dynamic model of platform productivity is established by using the nonlinear expectation theory. In addition, the Hamilton Jacobi Bellman equation (HJB equation) satisfied by the franchise value of platform developers is derived. Moreover, the impact of Knightian uncertainty on the optimal investment of investors, the franchise value of the platform, the marginal value of platform productivity, and the market clearing price of tokens is analyzed. Furthermore, the theoretical results are numerically simulated. The simulation shows that the optimal investment of investors in the platform and the franchise value of the platform are affected not only by the issuance of platform tokens, but also by the Knightian uncertainty. As the Knightian uncertainty degree increases, the optimal investment and franchise value of the platform decrease. Therefore, in addition to paying attention to the token issuance strategy of the platform itself, the operators of the platform also need to consider the impact of Knightian uncertain factors on the operation of the platform.

Key words: token, blockchain, platform finance, Knightian uncertainty, nonlinear expectation；stochastic optimization

摘要： 平台运营中投资者的投资效率冲击对平台生产力产生影响，从而对平台代币发行策略、代币价格以及平台特许经营价值产生影响。考虑投资者的投资效率冲击具有Knight不确定性时，利用非线性期望理论建立平台生产力动力学模型，并导出平台开发者特许经营价值所满足的哈密尔顿-雅克比-贝尔曼方程（HJB方程）。进而，分析Knight不确定对投资者最优投资、平台的特许经营价值、平台生产力的边际价值以及代币的市场出清价格的影响。最后，对所得理论结果进行数值模拟。分析表明：投资者对平台的最优投资、平台的特许经营价值除了受到平台代币的发行量影响，还会受到Knight不确定程度的影响，Knight不确定程度越大，平台的最优投资和平台的特许经营价值越小。因此，对于平台的经营者，除了注重对平台本身的代币发行策略管理外，还需要考虑Knight不确定因素对平台运营的影响。

关键词: 代币, 区块链, 平台金融, Knight不确定性, 非线性期望, 随机最优化