Coherent Risk Measures: Spectral Approach

This lecture by the instructor covers the concept of coherent risk measures, focusing on the spectral approach to risk aversion. It delves into defining risk in a rigorous way, the diversification principle, Value at Risk (VaR), Expected Shortfall (ES), and the advantages and drawbacks of VaR. The lecture explores the subadditivity axiom, capital allocation, and the importance of convex risk surfaces. It also discusses the creation of new coherent risk measures through convex combinations and the estimation of spectral measures of risk. The presentation concludes with examples illustrating risk aversion functions and the implications of different risk measures on portfolio optimization.