Machine learning for financial engineering

Contents......Page 10
Preface......Page 6
 1.1. Introduction and Historical Overview......Page 12
  1.2.1. Discrete Time......Page 17
  1.2.2. Continuous-Time......Page 30
 1.3. The GOP as an Investment Strategy......Page 41
  1.3.1. Is the GOP Better? – The Samuelson Controversy......Page 43
   1.3.2.1. Discrete time......Page 53
   1.3.2.2. Continuous time......Page 56
  1.3.3. How Long Does it Take for the GOP to Outperform other Portfolios?......Page 60
 1.4. The GOP and the Pricing of Financial Assets and Derivatives......Page 63
   1.4.1.1. Utility-Based Pricing......Page 66
   1.4.1.2. The Minimal Martingale Measure......Page 67
   1.4.1.3. Good-Deal Bounds......Page 68
  1.4.2. A World Without a Risk-Neutral Measure......Page 69
 1.5. Empirical Studies of the GOP......Page 73
   1.5.1.1. Discrete-Time Models......Page 74
   1.5.1.2. Continuous Time Models......Page 77
 1.6. Conclusion......Page 78
 References......Page 79
 2.1. Introduction......Page 92
 2.2. Constantly-Rebalanced Portfolio Selection......Page 95
  2.2.1. Log-Optimal Portfolio for Memoryless Market Process......Page 96
  2.2.2. Examples for the Constantly-Rebalanced Portfolio......Page 100
  2.2.3. Semi-Log-Optimal Portfolio......Page 109
  2.3.1. Log-Optimal Portfolio for Stationary Market Process......Page 110
  2.3.2. Empirical Portfolio Selection......Page 113
  2.3.3. Regression Function Estimation......Page 114
  2.3.4. Histogram-Based Strategy......Page 117
  2.3.5. Kernel-Based Strategy......Page 119
  2.3.6. Nearest-Neighbor-Based Strategy......Page 121
  2.3.7. Numerical Results on Empirical Portfolio Selection......Page 122
 References......Page 126
 3.1. Introduction......Page 130
 3.2. Mathematical Setup: Investment with Proportional Transaction Cost......Page 132
 3.3. Experiments on Heuristic Algorithms......Page 137
 3.4. Growth-Optimal Portfolio Selection Algorithms......Page 140
 3.5. Portfolio Selection with Consumption......Page 147
 3.6. Proofs......Page 152
 References......Page 161
 4.1. Introduction......Page 164
 4.2. Non-Leveraged, Long-Only Investment......Page 166
  4.3.1. No-Ruin Constraints......Page 173
  4.3.2. Optimality Condition for Short Selling with Cash Account......Page 176
  4.4.1. No-Ruin Condition......Page 181
  4.4.2. Kuhn–Tucker Characterization......Page 182
 4.5. Short Selling and Leverage......Page 183
 4.6. Experiments......Page 185
 References......Page 188
 5.1. Introduction......Page 190
  5.2.1. The Regression Problem......Page 193
  5.2.2. Regression Function Estimation and L2 Error......Page 194
  5.2.3. Partitioning Estimate......Page 195
  5.2.4. Kernel Estimate......Page 199
  5.2.5. Nearest-Neighbor Estimate......Page 202
  5.2.6. Empirical Error Minimization......Page 205
  5.3.1. Partition-Based Prediction Strategies......Page 213
  5.3.2. Kernel-Based Prediction Strategies......Page 220
  5.3.3. Nearest-Neighbor-Based Prediction Strategy......Page 222
  5.3.4. Generalized Linear Estimates......Page 223
  5.4.1. Partition-Based Prediction Strategies......Page 224
  5.4.2. Kernel-Based Prediction Strategies......Page 231
  5.4.4. Generalized Linear Estimates......Page 232
  5.4.5. Prediction of Gaussian Processes......Page 233
 References......Page 235
 6.1. Introduction: The Valuation of Option Price......Page 238
  6.1.2. Optimal Stopping......Page 239
  6.1.3. Martingale Approach: The Primal-Dual Problem......Page 240
  6.1.4. Lower and Upper Bounds of qt(x)......Page 241
  6.1.5. Sampling......Page 243
  6.1.6. Empirical-Pricing and Optimal Exercising of American Options......Page 244
  6.2.1. Estimating qt......Page 245
  6.2.2. Estimating the Lower and Upper Bounds of qt(x)......Page 246
  6.2.3. The Growth Rate of an Asset and the Black–Scholes Model......Page 248
 6.3. Nonparametric Regression Estimation......Page 252
  6.4.1. The Backward-Recursive Estimation Scheme......Page 255
  6.4.2. The Longsta –Schwartz (LS) method......Page 256
  6.4.3. A New Estimator......Page 257
 References......Page 258
Index......Page 260