Exploratory Mean-Variance Portfolio Optimization with Regime-Switching Market Dynamics

Considering the continuous-time Mean-Variance (MV) portfolio optimization problem, we study a regime-switching market setting and apply reinforcement learning (RL) techniques to assist informed exploration within the control space. We introduce and solve the Exploratory Mean Variance with Regime Switching (EMVRS) problem. We also present a Policy Improvement Theorem. Further, we recognize that the widely applied Temporal Difference (TD) learning is not adequate for the EMVRS context, hence we consider Orthogonality Condition (OC) learning, leveraging the martingale property of the induced optimal value function from the analytical solution to EMVRS. We design a RL algorithm that has more meaningful parameterization using the market parameters and propose an updating scheme for each parameter. Our empirical results demonstrate the superiority of OC learning over TD learning with a clear convergence of the market parameters towards their corresponding ``grounding true" values in a simulated market scenario. In a real market data study, EMVRS with OC learning outperforms its counterparts with the highest mean and reasonably low volatility of the annualized portfolio returns.

A Co-Prime Blur Scheme for Data Security in Video Surveillance

This paper presents a novel Coprime Blurred Pair (CBP) model for visual data-hiding for security in camera surveillance. While most previous approaches have focused on completely encrypting the video stream, we introduce a spatial encryption scheme by blurring the image/video contents to create a CBP. Our goal is to obscure detail in public video streams by blurring while allowing behavior to be recognized and to quickly deblur the stream so that details are available if behavior is recognized as suspicious. We create a CBP by blurring the same latent image with two unknown kernels. The two kernels are coprime when mapped to bivariate polynomials in the z domain. To deblur the CBP we first use the coprime constraint to approximate the kernels and sample the bivariate CBP polynomials in one dimension on the unit circle. At each sample point, we factor the 1D polynomial pair and compose the results into a 2D kernel matrix. Finally, we compute the inverse Fast Fourier Transform (FFT) of the kernel matrices to recover the coprime kernels and then the latent video stream. It is therefore only possible to deblur the video stream if a user has access to both streams. To improve the practicability of our algorithm, we implement our algorithm using a graphics processing unit (GPU) to decrypt the blurred video streams in real-time, and extensive experimental results demonstrate that our new scheme can effectively protect sensitive identity information in surveillance videos and faithfully reconstruct the unblurred video stream when two blurred sequences are available.