Machine Learning for Financial Engineering - Gyorfi, Laszlo (World Scientific, 2012)
5.4. Universally Consistent Predictions: Unbounded Y.
Preface; Contents; 1. On the History of the Growth-Optimal Portfolio M.M. Christensen; 1.1. Introduction and Historical Overview; 1.2. Theoretical Studies of the GOP; 1.2.1. Discrete Time; 1.2.2. Continuous-Time; 1.3. The GOP as an Investment Strategy; 1.3.1. Is the GOP Better? -- The Samuelson Controversy; 1.3.2. Capital Growth and the Mean-Variance Approach; 1.3.2.1. Discrete time; 1.3.2.2. Continuous time; 1.3.3. How Long Does it Take for the GOP to Outperform other Portfolios?; 1.4. The GOP and the Pricing of Financial Assets and Derivatives; 1.4.1. Incomplete Markets
1.4.1.1. Utility-Based Pricing1.4.1.2. The Minimal Martingale Measure; 1.4.1.3. Good-Deal Bounds; 1.4.2. A World Without a Risk-Neutral Measure; 1.5. Empirical Studies of the GOP; 1.5.1. Composition of the GOP; 1.5.1.1. Discrete-Time Models; 1.5.1.2. Continuous Time Models; 1.6. Conclusion; References; 2. Empirical Log-Optimal Portfolio Selections: A Survey L. Gyorfi, Gy. Ottucsak and A. Urban; 2.1. Introduction; 2.2. Constantly-Rebalanced Portfolio Selection; 2.2.1. Log-Optimal Portfolio for Memoryless Market Process; 2.2.2. Examples for the Constantly-Rebalanced Portfolio
2.2.3. Semi-Log-Optimal Portfolio2.3. Time-Varying Portfolio Selection; 2.3.1. Log-Optimal Portfolio for Stationary Market Process; 2.3.2. Empirical Portfolio Selection; 2.3.3. Regression Function Estimation; 2.3.4. Histogram-Based Strategy; 2.3.5. Kernel-Based Strategy; 2.3.6. Nearest-Neighbor-Based Strategy; 2.3.7. Numerical Results on Empirical Portfolio Selection; References; 3. Log-Optimal Portfolio-Selection Strategies with Proportional Transaction Costs L. Gyorfi and H. Walk; 3.1. Introduction; 3.2. Mathematical Setup: Investment with Proportional Transaction Cost
3.3. Experiments on Heuristic Algorithms3.4. Growth-Optimal Portfolio Selection Algorithms; 3.5. Portfolio Selection with Consumption; 3.6. Proofs; References; 4. Growth-Optimal Portfolio Selection with Short Selling and Leverage M. Horvath and A. Urban; 4.1. Introduction; 4.2. Non-Leveraged, Long-Only Investment; 4.3. Short Selling; 4.3.1. No-Ruin Constraints; 4.3.2. Optimality Condition for Short Selling with Cash Account; 4.4. Long-Only Leveraged Investment; 4.4.1. No-Ruin Condition; 4.4.2. Kuhn-Tucker Characterization; 4.5. Short Selling and Leverage; 4.6. Experiments; References