Financial Optimization and Risk Management under Uncertainty

This course introduces modern optimization methods a financial context. All optimization techniques will be motivated through practical decision problems. Starting with a review of scenario tree-based stochastic programming, we will then explore various methods of robust and distributionally robust optimization. Emphasis will be placed on the modeling of risk and uncertainty. We will see that uncertainty models should be chosen in light of the prior information available to the modeler. We will also see that different uncertainty models result in optimization models with different tractability properties. At the beginning of the course we will mainly focus on static models. Later on we will also investigate computationally tractable approaches for dynamic decision making under uncertainty. Day 1: Introduction/Review of Stochastic Programming Day 2: Robust Portfolio Optimization Day 3: Distributionally Robust Portfolio Optimization Day 4: Growth-Optimal Portfolio Theory Day 5: Dynamic Optimization under Uncertainty with Decision Rules

Seminar bestående av forelesninger og øvinger med case-studier. Til case-studiene trenger studentene tilgang til datamaskin med internettforbindelse og nødvendig software, f.eks. Matlab. I forbindelse med case-studiene skal studentene skrive korte rapporter og holde mindre presentasjoner.