The Mathematics of Financial Modelingand Investment Management

Index Page 772 Wednesday, February 4, 2004 1:13 PM

772 Index

Portfolios (Cont.)

selection, 500–503

global probabilistic frame-

work, 490–491

mean-variance analysis, 471

size, impact, 556–560

strategy. See Active portfolio;

Dedicated portfolio strat-

egy; Passive portfolio;

Structure portfolio

selection. See Investment

management process

tilting, 587–589

tracking errors, 558

Positive Itô process, 455

Positive theory, 472

Poterba, J., 343

Potters, M., 329

Power laws

distributions, 351

absence. See Scaling

truncation, 367

Power series, 122, 290

Power utility function, 489

Power-law distributions, 356–358

Power-law tail, 373

Predicted tracking error, 556, 565

Preferred habitat theory, 613, 618

Preferred stock, 25

Premium leg, 680

Premium par yield, 598

Prepayment, 56

option, 56

Priaulet, Philippe, 632, 633

Priaulet, Stéphanie, 632, 633

Price/earnings factor, 520

Price/earnings ratio, 519, 532

Prices. See Clean price; Dirty price

ARDL models, 546

diffusion, 78–80

discovery process, 26

dynamic models, 538–546

exponential divergence, 539

momentum, 572

nonlinear dynamic models,

546–549

persistence, 572

processes, sum, 444

risk, reduction, 59

Price-to-book value multiplier, 567

Price-to-book value per share

(P/B) ratio, 561, 563

calculation, 562

Price-to-earnings value multi -

plier, 567

Pricing. See Arbitrage pricing

generalizing. See European

options

model. See Baskets

relationships, 405–414

examples, 406–414

theory, defining, 455

Primal problem, 210

Primal-dual gap, 210

Primary market, 25

Primitive integral. See Functions

Principal, 52

Principal components analysis (PCA)

model, 335–338

usage, 536

Principal repayment, 56

Probabilistic dynamics, 168

Probabilistic judgments, 167

Probabilistic representation. See

Financial markets

Probability, 170–171. See also

Conditional probability

axiomatic theory, 169

concepts, 165

curves. See Default probability

density. See n-dimensional

probability density

function, time-evolution, 260

disjoint additivity, 171

distribution, evolution, 93

explanation, 167–169

framework, 92

interpretations, 166–167

measure, 441, 642. See also Arti -

ficial probability measure

space, 165, 170, 178, 402

representation, 430

sum, 704

theory, 165–173

development, 80, 737

Processes. See Stochastic pro -

cesses

drif, 279

innovation, 310–311

stochastic interval, defining,

220



volatility, 279

Product market, 21

Product rule, 109

Profit opportunities, reduction, 575

Program trades, 50

Proper subsets, 93–95

Property and casualty (P&C)

companies, 41

Proportionality recovery assump -

tion, 709

Protection buyer. See Lump-sum

payment

Protection leg, 680

Pure bond index matching, 650

Pure expectation theory, 613–617

Pure growth stocks, 563

Pure risk-free discount bond, 606

Put option, 64

Put price, 56

Putable bond, 56

Quadratic optimization prob -

lem, 486

Quadratic Programming (QP),

202, 211–212

Quadratic utility function, 489

Quadratic variation, 221–222

Quah, D., 334

Qualitiative information, inte -

gration, 15–17

Quality risk, 653

Quantile plot, 374

Quantile transformation, 369

Quantitative finance, 283

Quantitative information, inte -

gration, 15–17

Quantitative methods, usage, 14

Quantitative phenomena, dynam -

ics, 96–97

Quantities, 96–100

Quantum physics, 444

Quarterly Derivatives Report,

U.S. Office of the Control-

ler of the Currency, 745

Quotient rule, 109, 113

Rachev, S.T., 189, 329, 389

Radon-Nikodym derivative, 416–

417, 464

definition, 458

usage, 467. See also Continu-

ous-state setting

Ramaswamy, Krishna, 520

Rand Corporation, 82

Random disturbance, 80

Random interest rates, 716

Random matrices, 329–332

relationship. See Capital Asset

Pricing Model

Random Matrices Theory (RMT),

329



Random Matrix Theory (RMT),

522



Random phenomena, evolution, 93

Random shocks

accumulation, 217

feedback, 220

Random variables, 32, 172–

175. See also Normal
     random variable
     convergence, 189–190
     distribution
     convergence, 190–191
     functions, 177
     joint probability, 176
     probability density, 352
     sequences, 189–191
     Random vectors, 175–178
     Random walk, 221. See also
     Arithmetic random walk;
     Computer-generated
     independent arithmetic
     random walks; Corre-
     lated random walks; Dis-
     crete random walk
     hypothesis, 343
     models, 324–327. See also Mul-
     tivariate random walk
     model
     empirical adequacy, 327
     Range notes, 54