Portfolio optimization in a market with hidden Gaussian drift and randomly arriving expert opinions
研究投资者在股票收益受隐藏均值回归漂移影响的市场中，如何利用来自收益和随机到达的专家意见进行最优投资组合选择，通过卡尔曼滤波估计漂移并用动态规划求解效用最大化问题。
Abstract This paper investigates the optimal selection of portfolios for power utility maximizing investors in a financial market where stock returns depend on a hidden Gaussian mean reverting drift process. Information on the drift is obtained from returns and expert opinions in the form of noisy signals about the current state of the drift arriving randomly over time. The arrival dates are modeled as the jump times of a homogeneous Poisson process. Applying Kalman filter techniques we derive estimates of the hidden drift which are described by the conditional mean and covariance of the drift given the observations. The utility maximization problem is solved with dynamic programming methods. The associated dynamic programming equation is a partial integro-differential equation and degenerate in the diffusion part of the differential operator. We therefore adopt a regularization approach and add a Brownian perturbation to the state process, scaled by a small parameter that approaches zero. We prove that the value functions of the regularized problems converge to the value function of the original problem. This enables the construction of $$\varepsilon $$ -optimal strategies.