Stochastic Optimization: Portfolio Optimization

This lecture covers stochastic optimization in the context of portfolio optimization, focusing on decision criteria for uncertain objective functions, including expected value, variance, value-at-risk, conditional value-at-risk, and mean-variance functional. The instructor explains different models for portfolio optimization under uncertainty, such as minimizing expected portfolio loss, minimizing variance of portfolio loss, and minimizing a mean-variance functional. The lecture also delves into the concept of conditional value-at-risk (CVaR) and its applications in quantifying risk in portfolio management, with detailed proofs and examples illustrating how CVaR splits the atom in risk assessment.