Optimization under Uncertainty using GAMS: Success Stories and ...

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<strong>Optimization</strong> Models in Finance “Static” models: The decision is made once, no further changes possible Mean-Variance Models Portfolio Models for Fixed Income Indexation Models (“Tracking Models”) Scenario based <strong>Optimization</strong> “Dynamic” models: Sequence of decisions Stochastic Programming 10
Mean-Variance Model Markowitz (1952)Nobel prize 1990 Some investments x i with historical data: Expected returns of investments: µ i : Mean of historical returns Risk: Variance of investments Q i,j Goal: Balance risk r of portfolio against expected returns of portfolio Minimize variance v of portfolio for a given target return r 11
Page 1 and 2: Optimization under Uncertainty usin
Page 3 and 4: GAMS Development Corp. & GAMS Softw
Page 5 and 6: What are Algebraic Modeling Languag
Page 7 and 8: GAMS Basic Principles Balanced mix
Page 9: Uncertainty in Finance Very active
Page 13 and 14: Mean-Variance Model Core GAMS Model
Page 15 and 16: Mean-Variance Model Procedural Elem
Page 17 and 18: Mean-Variance Model Extensions Dif
Page 19 and 20: Trading Restrictions - Formulation
Page 21 and 22: Recent Developments Support of cod
Page 23 and 24: 4 A simple Scenario Tree 0 1 2 5 6
Page 25 and 26: Stochastic Programming Some Challen
Page 27 and 28: Facing these (tech.) Challenges 1.
Page 29 and 30: Scenario Reduction Goal: Find an a
Page 31 and 32: Specialized Algorithms OSL Stochast
Page 33 and 34: Main Problem: Specialized Algorithm

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