Machine Learning for Financial Engineering.

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.

5. Nonparametric Sequential Prediction of Stationary Time Series L. Gyorfi and Gy. Ottucsak5.1. Introduction; 5.2. Nonparametric Regression Estimation; 5.2.1. The Regression Problem; 5.2.2. Regression Function Estimation and L2 Error; 5.2.3. Partitioning Estimate; 5.2.4. Kernel Estimate; 5.2.5. Nearest-Neighbor Estimate; 5.2.6. Empirical Error Minimization; 5.3. Universally Consistent Predictions: Bounded Y; 5.3.1. Partition-Based Prediction Strategies; 5.3.2. Kernel-Based Prediction Strategies; 5.3.3. Nearest-Neighbor-Based Prediction Strategy; 5.3.4. Generalized Linear Estimates.

5.4. Universally Consistent Predictions: Unbounded Y.

This volume investigates algorithmic methods based on machine learning in order to design sequential investment strategies for financial markets. Such sequential investment strategies use information collected from the market's past and determine, at the beginning of a trading period, a portfolio; that is, a way to invest the currently available capital among the assets that are available for purchase or investment. The aim is to produce a self-contained text intended for a wide audience, including researchers and graduate students in computer science, finance, statistics, mathematics, and eng.

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