Ralph Vince - Portfolio Mathematics

JWDD035-Ind JWDD035-Vince February 22, 2007 17:38 Char Count= 0

418 INDEX

Distributions.See also(Continued)

nonstationary, 26

open-ended, 45

probability, 43–98

stationary, 26, 52

unimodal, 54

Downhill Simplex (mathematical

minimization routine), 409

Drawdown

management, 359–363

optimality, 361

risk of, 389–414

Java code for determining,

392–395

time spent in, 197–198

Dynamic fractionalfstrategy, 325

Dynamic hedging, 335–340

Eckhardt, William, 372

Efficient frontier, 234, 264, 265

geometric, 266–273

Ergodicity, 16

E–V theory (Markowitz), 235–237,

240–241, 263.See alsoModern

Portfolio Theory

Exact sequences, 8–12

Expectation, mathematical, 6–8

Expected average compound growth

(EACG), maximizing, 209–217,

345

Expected Utility Theorem, 218, 221

Exponential Distribution, 54, 55, 83–87

Negative, 85

F Distribution, 94

fshift, 342–343

Fisher’s Z transformation, 40–41

Football pools, 21

Galton’s board, 52, 53

Gamma Distribution, 97

Gauss, Karl Friedrich, 52

Gaussian distribution.SeeNormal

Distribution

Genetic algorithm, 317–321

Geometric average trade, 127–128

Geometric Distribution, 78–80

Geometric growth concepts,

103–116

Geometric mean, 46, 47, 103–109

calculation of using spreadsheet

logic, 127

estimating, 107–109, 198–201

finding optimalfby, 122–125

Gradient trading, 345–351

Growth risk ratio, 354–355

Growth, utility, and finite streams, laws

of, 207–229

expected average compound

growth, maximizing, 209–217

Expected Utility Theorem, 218

utility and the new framework,

226–229

utility preference curve, finding,

222–226

utility preference functions,

characteristics of, 218–221

utility theory, 217–218

alternate arguments to, 221–222

Haight, Frank, 97–98

Harmonic mean, 46, 47

Horse racing, and pari-mutuel betting,

23–24

House advantage, 15–17, 19–20

Hypergeometric Distribution, 80–81

Inflection, point of, 355–358

Kelly Betting System, 119

Kelly criterion, xvii, 120

Kelly formula, 24, 120–122, 131

Kelly, John L., Jr., 119

Kurtosis, 51

Lagrange, method of, 241–246

Laplace, Pierre Simon, 3

Law of Averages, 15, 16

Leverage Space Model, xvii, xx,

287–322, 376

genetic algorithm, 317–321

important notes, 321–322