标题： 在部分信息下大型投资者控制市场情绪的投资组合优化 显示英文标题

标题： Portfolio optimization for a large investor controlling market sentiment under partial information

摘要： 我们考虑一个投资者面临的效用最大化问题，其中风险资产价格过程具有由不可观测的连续时间有限状态马尔可夫链影响的纯跳跃动态，其强度也可以通过投资者的行为进行控制。 使用经典滤波理论，我们将具有部分信息的问题简化为具有完全信息的问题，并针对对数和幂效用函数进行求解。 特别是，我们将用于分段确定性马尔可夫过程（PDMP）的控制理论应用于我们的问题是，推导出价值函数的最优性方程，并将价值函数表征为相关动态规划方程的唯一粘性解。 最后，我们提供了一个简单的例子，其中不可观测的状态过程由一个两状态马尔可夫链驱动，并讨论了投资者控制状态过程强度的能力如何影响在部分信息和完全信息情况下最优投资组合策略以及最优财富。 显示英文摘要

摘要： We consider an investor faced with the utility maximization problem in which the risky asset price process has pure-jump dynamics affected by an unobservable continuous-time finite-state Markov chain, the intensity of which can also be controlled by actions of the investor. Using the classical filtering theory, we reduce this problem with partial information to one with full information and solve it for logarithmic and power utility functions. In particular, we apply control theory for piecewise deterministic Markov processes (PDMP) to our problem and derive the optimality equation for the value function and characterize the value function as the unique viscosity solution of the associated dynamic programming equation. Finally, we provide a toy example, where the unobservable state process is driven by a two-state Markov chain, and discuss how investor's ability to control the intensity of the state process affects the optimal portfolio strategies as well as the optimal wealth under both partial and full information cases.