SIAM Journal on Control and Optimization, Volume 58, Issue 6, Page 3041-3061, January 2020.
We study the mean-variance portfolio selection problem for a class of price models, which well fit the two features of time-stamped transactions data. The price process of each stock is described by a collection of partially observed point processes. They are the noisy observation of an intrinsic value process, assumed to be Markovian. However, the control problem with partial information is non-Markovian and depends on an infinite-dimensional measure-valued input. To solve the challenging problem, we first establish a separation principle, which divides the filtering and the control problems and reduces the infinite-dimensional input to finite-dimensional ones. Building upon the result of nonlinear filtering with counting process observations, we solve the control problem by employing the stochastic maximum principle for control with forward-backward SDEs developed in [SIAM J. Control Optim., 48 (2009), pp. 2945--2976]. We explicitly obtain the efficient frontier and derive the optimal strategy, which is based on the filtering estimators.

中文翻译：

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部分观测点过程的均值方差投资组合选择

SIAM控制与优化杂志，第58卷，第6期，第3041-3061页，2020年1月。
我们研究了一类价格模型的均值方差投资组合选择问题，该问题非常适合带有时间戳的交易数据的两个特征。每只股票的价格过程通过部分观察点过程来描述。他们是内在价值过程的嘈杂观察，假定是马尔可夫模型。但是，具有部分信息的控制问题是非马尔可夫问题，并且取决于无穷维度量值输入。为了解决这一难题，我们首先建立了分离原理，将滤波问题和控制问题分开，并将无穷维输入减少为无穷维输入。以对过程观察计数的非线性滤波结果为基础，我们采用[SIAM J. Control Optim。，48（2009），pp。2945--2976]中开发的向前-向后SDE进行控制的最大随机原理来解决控制问题。我们明确地获得了有效的边界并得出了基于滤波估计量的最优策略。