AI 中文总结
研究双边数据市场平台的连续时间动态定价问题，通过建模供应商和消费者到达过程，将其问题表述为随机控制问题并推导HJB方程，证明值函数性质，验证最优策略，还进行数值分析考察参数对策略的影响。
AI 中文摘要
我们研究了一个数据平台的连续时间动态定价问题，该平台从对隐私敏感的供应商处购买原始数据，并向消费者销售数据产品。平台控制向供应商提供的收购价格和向消费者收取的销售价格。供应商和消费者的到达由点过程建模，其强度取决于平台当前的数据存量，体现了数据积累与市场参与之间的反馈。我们将平台问题表述为具有跳跃扩散状态过程的无限期随机控制问题，并推导相关的非线性积分-微分HJB方程。我们证明了值函数是唯一的粘性解，在适当条件下建立了经典正则性，并验证了最优反馈定价策略。最后，我们进行数值分析，以检验模型参数对最优定价策略的影响。
英文摘要
We study a continuous-time dynamic pricing problem for a data platform that purchases raw data from privacy-sensitive providers and sells data products to consumers. The platform controls both the acquisition price offered to providers and the selling price charged to consumers. Provider and consumer arrivals are modeled by point processes whose intensities depend on the platform's current data stock, capturing feedback between data accumulation and market participation. We formulate the platform's problem as an infinite-horizon stochastic control problem with a jump-diffusion state process and derive the associated nonlinear integro-differential HJB equation. We prove that the value function is the unique viscosity solution, establish classical regularity under suitable conditions, and verify the optimal feedback pricing policy. Finally, we conduct numerical analyses to examine the influences of model parameters on the optimal pricing policies.
