volatility forecasting into two pillars: the realized variances and realized correlations and quantifies the corresponding …% and at least 78%). The results on the GMV portfolios show that realized covariance models exhibit lower ex-post volatility …

, transaction costs, and stochastic volatility. Determining the dynamic optimal portfolio in this general setting is almost always … intractable. We propose a multiscale asymptotic expansion when the volatility process is characterized by its time scales of … fluctuation. The analysis of the nonlinear Hamilton- Jacobi-Bellman PDE is a singular perturbation problem when volatility is fast …