Active and passive portfolio management with latent factors

We address a portfolio selection problem that combines active (outperformance) and passive (tracking) objectives using techniques from convex analysis. assume general semimartingale market model where the assets' growth rate processes are driven by latent factor. Using analysis we obtain closed-form solution for optimal provide theorem establishing its uniqueness. The motivation incorporating factors is to achieve improved estimation, an otherwise notoriously difficult task. To this end, focus on rates unobservable Markov chain. in case requires filtering step posterior probabilities state of chain asset price information, which subsequently used find allocation. show strategy average strategies investor would have held each assuming remains state. Finally, implement number historical backtests demonstrate performance portfolio.