  This survey reviews portfolio choice in settings where investment
opportunities are stochastic due to, e.g., stochastic volatility or return
predictability. It is explained how to heuristically compute candidate optimal
portfolios using tools from stochastic control, and how to rigorously verify
their optimality by means of convex duality. Special emphasis is placed on
long-horizon asymptotics, that lead to particularly tractable results.

Portfolio Management;Optimization and Control