Optimal Portfolio Strategy

Dynamic Factor Models with Forward-Looking Views ArXiv ID: 2509.11528 “View on arXiv” Authors: Anas Abdelhakmi, Andrew E. B. Lim Abstract Prediction models calibrated using historical data may forecast poorly if the dynamics of the present and future differ from observations in the past. For this reason, predictions can be improved if information like forward looking views about the state of the system are used to refine the forecast. We develop an approach for combining a dynamic factor model for risky asset prices calibrated on historical data, and noisy expert views of future values of the factors/covariates in the model, and study the implications for dynamic portfolio choice. By exploiting the graphical structure linking factors, asset prices, and views, we derive closed-form expressions for the dynamics of the factor and price processes after conditioning on the views. For linear factor models, the price process becomes a time-inhomogeneous affine process with a new covariate formed from the views. We establish a novel theoretical connection between the conditional factor process and a process we call a Mean-Reverting Bridge (MrB), an extension of the classical Brownian bridge. We derive the investor’s optimal portfolio strategy and show that views influence both the myopic mean-variance term and the intertemporal hedge. The optimal dynamic portfolio when the long-run mean of the expected return is uncertain and learned online from data is also derived. More generally, our framework offers a generalizable approach for embedding forward-looking information about covariates in a dynamic factor model. ...

Optimal Trading under Instantaneous and Persistent Price Impact, Predictable Returns and Multiscale Stochastic Volatility ArXiv ID: 2507.17162 “View on arXiv” Authors: Patrick Chan, Ronnie Sircar, Iosif Zimbidis Abstract We consider a dynamic portfolio optimization problem that incorporates predictable returns, instantaneous transaction costs, price impact, and stochastic volatility, extending the classical results of Garleanu and Pedersen (2013), which assume constant volatility. Constructing the optimal portfolio strategy in this general setting is challenging due to the nonlinear nature of the resulting Hamilton-Jacobi-Bellman (HJB) equations. To address this, we propose a multi-scale volatility expansion that captures stochastic volatility dynamics across different time scales. Specifically, the analysis involves a singular perturbation for the fast mean-reverting volatility factor and a regular perturbation for the slow-moving factor. We also introduce an approximation for small price impact and demonstrate its numerical accuracy. We formally derive asymptotic approximations up to second order and use Monte Carlo simulations to show how incorporating these corrections improves the Profit and Loss (PnL) of the resulting portfolio strategy. ...