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Epps T. — Quantitative Finance: Its Development, Mathematical Foundations, and Current Scope
Epps T. — Quantitative Finance: Its Development, Mathematical Foundations, and Current Scope

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Название: Quantitative Finance: Its Development, Mathematical Foundations, and Current Scope

Автор: Epps T.

Аннотация:

A rigorous, yet accessible, introduction to essential topics in mathematical financePresented as a course on the topic, Quantitative Finance traces the evolution of financial theory and provides an overview of core topics associated with financial investments. With its thorough explanations and use of real-world examples, this book carefully outlines instructions and techniques for working with essential topics found within quantitative finance including portfolio theory, pricing of derivatives, decision theory, and the empirical behavior of prices.The author begins with introductory chapters on mathematical analysis and probability theory, which provide the needed tools for modeling portfolio choice and pricing in discrete time. Next, a review of the basic arithmetic of compounding as well as the relationships that exist among bond prices and spot and forward interest rates is presented.? Additional topics covered include:Dividend discount modelsMarkowitz mean-variance theoryThe Capital Asset Pricing ModelStatic?portfolio theory based on the expected-utility paradigmFamiliar probability models for marginal distributions of returns and the dynamic behavior of security pricesThe final chapters of the book delve into the paradigms of pricing and present the application of martingale pricing in advanced models of price dynamics. Also included is a step-by-step discussion on the use of Fourier methods to solve for arbitrage-free prices when underlying price dynamics are modeled in realistic, but complex ways.Throughout the book, the author presents insight on current approaches along with comments on the unique difficulties that exist in the study of financial markets. These reflections illustrate the evolving nature of the financial field and help readers develop analytical techniques and tools to apply in their everyday work. Exercises at the end of most chapters progress in difficulty, and selected worked-out solutions are available in the appendix. In addition, numerous empirical projects utilize MATLAB® and Minitab® to demonstrate the mathematical tools of finance for modeling the behavior of prices and markets. Data sets that accompany these projects can be found via the book's FTP site.Quantitative Finance is an excellent book for courses in quantitative finance or financial engineering at the upper-undergraduate and graduate levels. It is also a valuable resource for practitioners in related fields including engineering, finance, and economics.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2009

Количество страниц: 401

Добавлена в каталог: 16.08.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Absolute continuity of functions      30
Absolute continuity of measures      24
Absolute risk aversion      108
Adapted process      171
Additively separable utility      198
Affine function      38 106
Allais' paradox      128
Almost everywhere      18
Almost sure/certain      26
apt      see "Arbitrage pricing theory"
Arbitrage portfolio      249
Arbitrage pricing theory, criticisms of      251
Arbitrage pricing theory, description      248
Arbitrage, defined      247
Arbitrage, pricing by      9 59 247
ARCH/GARCH models      310
ARMA Models      310
Asynchronous trading effect      158
Autocorrelation function      156
Bates model      see "SV-jump model"
Behavioral Finance      134
Bernoulli distribution      51
Beta coefficient      91
Bid-asked bounce      156
Bienayme — Galton — Watson process      324
Binomial distribution      51
Black — Scholes formulas      266 271
Black — Scholes formulas with time-varying volatility      349
Bonds, arbitrages among      252
Bonds, coupon      57 252
Bonds, default-free      58
Bonds, discount      57 252
Bonds, forward      63
Bonds, zero-coupon      57
Book-to-market anomaly      94 246
Borel sets      16
Borel — Cantelli lemma      44
Branching process model, description      324
Branching process model, option pricing under      343
Brownian motion, defined      167
Brownian motion, geometric      181 263
Brownian motion, properties of      167
Capital asset pricing model, multiperiod framework      219
Capital asset pricing model, single-period framework      87 245
Capital asset pricing model, tests of      92
CAPM      see "Capital asset pricing model"
Cauchy distribution      51 148 345
Central limit theorems      45
Certainty effect      129
Certainty equivalent      108
CEV model      see "Constant elasticity of variance"
Change-of-variable formula, multivariate      33
Change-of-variable formula, univariate      32
Characteristic function, applications in option pricing      339 351 354
Characteristic function, defined      336
Chi-squared distribution      151
Coefficient of variation      36
Common stock      6
Complete markets      302 326
Compound-events model      150 166
Compound-Poisson process      166
Conditional expectation, generally      38
Conditional expectation, process      267 351
Conditional expectation, tower property of      39 162 266
Conditional probability      26
Conditional variance      39
Constant elasticity of variance model      182 308
Contingent claims      3
Convergence in distribution      43
Convergence in probability      43
Convergence of sequences of functions      42
Convergence of sequences of numbers      42
Convergence, almost-sure      44
Convex function      37
Countable additivity      17
Countable set      15 29
Counting measure      17 26 30 31
Covariance matrix      38
Cox — Ingersoll — Ross model      301
Cumulant-generating function      46 153
Cumulative distribution function      29 32
Cumulative distribution function from characteristic function      339
Delta hedging      280
Delta of option      279
Derivative assets, defined      254
Descending factorial moments      41
Diffusion coefficient      181
Directing process      322
Discontinuous price processes      318
Dividend Discount Model      72 241
Dominated convergence      22 23 115
Drift term      181
Dynamic portfolio models      193 218
Dynamic pricing models      220 246 298
Dynamic programming      194
Early-exercise boundary      284
Efficiency of markets      139 160 229
Efficient portfolios      75
Ellsberg paradox      106
Equity premium      224
Equivalent measures      see "Measure(s)"
Euler's formula      336
Event studies      230
Excess volatility      225 237
Exchange-traded funds      6
Expected value      see "Mathematical expectation"
Expected-utility theory vs. mean-variance theory      117
Expected-utility theory, axioms      98
Expected-utility theory, criticisms of      127
Expected-utility theory, financial applications      103
Expected-utility theory, proof of theorem      101
Expected-utility theory, qualitative implications      109
Factor loading      80 248
Factor model      80 248
Fair-game property of martingales      162
Feynman — Kac solution      266 289
Field (of sets)      16
Filtration      171 267
Firm size anomaly      94 246
First-moment dependence      156 236
Fixed-income securities      6
Forward contract      63 255 269 296
Forward measure      302
Forward price      63 255
Forward rate      64
Fourier methods for pricing      339
Fourier transform      337 339
Fractals      170
Fubini's theorem      35
Fundamental PDE      264
Fundamental theorem of asset pricing      291
Futures contract      257 259
Gamma distribution      49 322
Gamma of option      279
Gamma process      322
Geometric Brownian motion      181 263
Girsanov's theorem      295 309 332
Growth optimality      see "Optimal growth"
Habit persistence      225
Hansen — Jagannathan bound      224
Heston model      348
Heston model, compared with jump diffusion      320
Heston model, description      312
Heston model, option pricing under      350
Hobson — Rogers model      309
Idiosyncratic risk      80 248
Implicit volatility      279 282 286 314 318 334
Independence of events      27
Independence of random variables      33
Independence of sigma fields      33
Indicator function      12
Infinite divisibility      166
Informational efficiency      229
Integral, Ito      178
Integral, Lebesgue      20
Integral, Lebesgue — Stieltjes      20 31 34
Integral, Riemann      18 179
Integral, Riemann — Stieltjes      19
Integral, Stochastic      178 183
Integral, Stratonovich      190
Intensity parameter      see "Poisson process"
Interest rate caps      7
Interest rate, compound      56
Interest rate, continuously compounded      56
Interest rate, forward      63
Interest rate, simple      55
Interest rate, spot      61
Inverse gaussian distribution      357
Ito process, defined      180
Ito process, quadratic variation of      182
Ito's formula for functions of a BM      185
Ito's formula, functions of jump diffusions      319 355
Ito's formula, functions of time and BM      186
Ito's formula, functions of time and Ito process      187
January effect      94 236
Jensen's inequality      37 107
Jump diffusion model, compared with Heston model      320
Jump diffusion model, description      318
Jump diffusion model, option pricing under      330 341
Kurtosis in stock returns      147
Kurtosis of normal distribution      47
Kurtosis, coefficient of      36
Lagrange multiplier      77
Law of total probability      27
Laws of large numbers      45 204
Lebesgue measure      17 26
Leverage effect      308
Lindeberg — Levy theorem      45
Lognormal distribution      48 143
Lucas model      220 236
Marginal distribution      32
Market portfolio      89
Markets for financial assets      4
Marking to market      257
Martingale measure, existence of      292
Martingale measure, uniqueness of      302 313 326
Martingale process in continuous time      171
Martingale process, conditional expectation as      267
Martingale process, defined      162
Martingale process, fair-game property      162 180
Martingale process, price as      162 223 292
Mathematical expectation, conditional      38
Mathematical expectation, generally      34
Mathematical expectation, properties of      36
Mean-reverting process      182 301 312
Mean-variance dominance      76
Mean-variance dominance in short holding periods      120
Mean-variance dominance, defined      117
Measurable function      20 28
Measurable space      25
Measure(s), $\sigma$-finite      17 23
Measure(s), absolutely continuous      24
Measure(s), changes of      23 41 290 295 299
Measure(s), equivalent      24 42 290
Measure(s), forward      302
Measure(s), generally      16
Measure(s), induced      28
Measure(s), monotone property of      17 26
Measure(s), natural      291
Mixture models      150 317 322
Moment-generating function      40 336
Moments      see "Random variables"
Momentum in prices      240
Money-market fund      62
Monks, self-flagellating      106
Monotone convergence      22
Monotone sequence of sets      17
Multiplication rule      27
Mutual funds      6
Natural measure      291
Normal distribution      46 143
Normative models      71
Null sets/events      26 27 33 290
Numeraire      291 300 330
Numerical integration      340
Operational vs. calendar time      322
Optimal growth in continuous time      206
Optimal growth in discrete time      203
Optimal growth, basic concept      201
Options, American      283
Options, Black — Scholes formulas      266
Options, bounds on prices      275
Options, calls      262 297
Options, deltas of      279
Options, digital      297 303
Options, European      262 297
Options, gammas of      279
Options, properties of prices      277
Options, put-call parity      276
Options, puts      262 270 297
Options, threshold      298
Order notation      12
Partition      27
Point process      165
Poisson distribution      52 150
Poisson process      318
Poisson process, defined      165
Poisson process, intensity parameter of      165 318 357
Portfolio insurance      281
Positive models      71 127
Preference reversals      131
Preferred stock      6
Pricing function      222
Pricing kernel      221
Primary assets      6
Principle of optimality      195
Probability density function      30
Probability generating function      41 325 343
Probability limit      44 178
Probability mass function      30
Probability measure      25
Probability space      25
Prospect theory      129 226
Put-call parity      276 277
Quadratic covariation      189 352
Quadratic programming      77
Quadratic variation      170 179 182 352
Radon — Nikodym derivative      24 30 31
Radon — Nikodym theorem      24 42
Random variables, continuous      29
Random variables, defined      28
Random variables, discrete      29
Random variables, mixed      29
Random variables, moments of      36
Random variables, supports of      29
Random-walk hypothesis      160 235
Rate of return, continuously compounded      140
Rate of return, simple      73
Rational expectations      139 217 229
Reflection effect      130
Regime-switching models      357
Regression function      38
Relative risk aversion      108
Replication and uniqueness of martingale measure      303
Replication, dynamic      262
Replication, infeasibility in jump models      326
Replication, infeasibility in SV models      313
Replication, static      256 261
Risk aversion and diminishing marginal utility      133
Risk aversion, measures of      107
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