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Shafer G., Vovk V. — Probability and finance
Shafer G., Vovk V. — Probability and finance



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Название: Probability and finance

Авторы: Shafer G., Vovk V.

Аннотация:

Probability and Finance is essential reading for anyone who studies or uses probability. Mathematicians and statisticians will find in it a new framework for probability: game theory instead of measure theory. Philosophers will find a surprising synthesis of the objective and the subjective. Practitioners, especially in financial engineering, will learn new ways to understand and sometimes eliminate stochastic models.
The first half of the book explains a new mathematical and philosophical framework for probability, based on a sequential game between an idealized scientist and the world. Two very accessible introductory chapters, one presenting an overview of the new framework and one reviewing its historical context, are followed by a careful mathematical treatment of probability's classical limit theorems.
The second half of the book, on finance, illustrates the potential of the new framework. It proposes greater use of the market and less use of stochastic models in the pricing of financial derivatives, and it shows how purely game-theoretic probability can replace stochastic models in the efficient-market hypothesis.


Язык: en

Рубрика: Экономика и финансы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 414

Добавлена в каталог: 09.12.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Probability distribution stable      311
Probability finite or infinite horizon      10
Probability game      9 185
Probability game-theoretic      16
Probability lower      15 152 186
Probability measure      41
Probability measure equivalent      233
Probability measure-theoretic      40
Probability modern      35
Probability objective and subjective      19 34
Probability protocol      9 185
Probability protocol constant move spaces      90
Probability protocol symmetric      11 187
Probability space      169
Probability space filtered      169
Probability upper      15 152 186
Process bounded forecasting      66
Process increasing      82
Process measure-theoretic      169
Process partial      149
Process predictable      81 169
Process unbounded forecasting      81
Propensity      22
Protocol binary probability forecasting      177
Protocol Black — Scholes      217
Protocol coin-tossing      178
Protocol diffusion      337—338
Protocol fair-coin      127
Protocol Lindeberg      148
Protocol Lyapunov's      162
Protocol market      319
Protocol Poisson      304 306
Protocol probability      9 90 185
Protocol securities market      353
Protocol securities market abstract      360
Quadratic supervariation      91
Quadratic variation      91 338
Quadratic variation game-theoretic      118 174
Quadratic variation measure-theoretic      176
Quadratic variation optional      340
Quadratic variation predictable      340
Quantum mechanics as a game      190
Quantum mechanics challenge to determinism      8
Quantum mechanics fundamental interpretative hypothesis      20
Quantum mechanics open system      7
Quasi-Borel set      96
Radon — Nikodym theorem      42
Radon, Johann (1887—1956) measure theory      36
Random variable adapted sequence      169
Random variable definition      10 41 169
Random variable predictable sequence      169
Reality as part of World      7
Reality move space      90
Reality strategy      76 87
Regulated function      290
Reichenbach, Hans (1891—1953) collectives      47
Reichenbach, Hans (1891—1953) discussion with Borel      57
Relative frequency      18
Relative variation exponent      275
Relative variation sprectrum      259
Relatively continuous      275
Relatively continuous nonstandard function      286
Renyi, Alfred (1921—1970) conditional probability      42
Return on capital      368
Riemann, Bernhard (1826—1866) integration      36
Risk vs. return      367
Risk-adjusted probability      348
Risk-free bond      295
Risk-neutral probability      348
Risk-neutral valuation      233 348
Robinson, Abraham (1918—1974) life      283
Robinson, Abraham (1918—1974) nonstandard analysis      26 283
Robinson, Abraham (1918—1974) photograph      271
Sample space bounded forecasting      66
Sample space for market protocol      319
Sample space measure-theoretic      40
Sample space probability game      9
Samuelson, Paul A. (born 1915) efficient markets      227
Samuelson, Paul A. (born 1915) photograph      351
Saturation theorem      291
Savage, Leonard J. (1917—1971) conservation of fairness      56
Schal, Manfred discrete hedging      258
Scholes, Myron (born 1941) Black-Scholes formula      215
Scholes, Myron (born 1941) photograph      237
Schwarz, Gideon change of time      306
Schweizer, Martin (born 1961) discrete hedging      258
Scrap value      13
Securities market protocol abstract      360
Security derivative      23
Semimartingale game-theoretic      85
Semimartingale stochastic      315
Simulating transactions      12
Situation      10 90 183
Situation bounded forecasting      66
Situation child      149
Situation divergent      66
Situation final      149
Situation follow      149
Situation in market protocol      319
Situation initial      10 149 183
Situation on path      149
Situation parent      91 149
Situation precede      66 149
Situation strictly follow      149
Situation strictly precede      149
Situation terminal      10
Situation unbounded forecasting      81
Skeptic gain function      150 183
Skeptic goal      90
Skeptic move space      90 150 183
Skeptic name for Player I      4
Skeptic real and imaginary      352 355
Skeptic strategy      66 76 81
Skorohod, Anatolii V. (born 1930) independent increments      314
Smoluchowski, Marian von (1872—1917) Brownian motion      204
Smooth function      127
Solomonoff, Ray J. (born 1926) inductive inference      50
Square as derivative      299
Stable law characteristic exponent      311
Stable law definition      311
Stable law tails      312
Standard      272
Standard function      273
Standard part      284
Statistical modeling      21
Statistical physics      35
Steinhaus, Hugo (1887—1966) revival of probability      35
Stewart, F.M. determinate games      97
Stochastic calculus      206
Stochastic differential equation      206 335
Stochastic function      274
Stochastic integral      340
Stochastic process      18
Stochastic volatility      230
Stochasticism      21
Stopping time      108 169
Stopping time complete      117
Stout, William F. (born 1940) iterated logarithm      99 173
Strategy      66
Strategy beginning in situation      150
Strategy Borel measurable      170
Strategy bounding      82
Strategy Forecaster's      178
Strategy intrinsic      322
Strategy Investor's in market protocol      319
Strategy market      322
Strategy Reality      87
Strategy Skeptic's      11 81 150 183
Strictly convex function      302
Strike price      216
Strong law of large numbers bounded      61
Strong law of large numbers finance-theoretic      356
Strong law of large numbers for martingales      90
Strong law of large numbers fuzzy      362
Strong law of large numbers Kolmogorov's      75
Strong price      328
Strong upper price      328
Strong variation      289
Stroock, Daniel W. (born 1940) weak solution      347
Submarket function      332
Subparabolic      138
Substochastic function      211 274
Super-replicate strongly      325
Super-replicate weakly      324
Super-replication game      325—327
Superior intelligence      8 34
Supermarket function      331
Supermartingale game-theoretic definition      82 184
Supermartingale witnessing      83
Superparabolic function      137
Superparabolic function smooth      139
Superstochastic function      274
Supervariation, quadratic      91
Symmetric probability protocol      11
Taqqu, Murad S. (born 1942) pathwise stochastic integration      349
Taylor, S. James (born 1929) strong variation      290
Ternary possibility      24
Tobin, James (born 1918) portfolio selection      199
topology      96
Transfer principle      26 286
Tree binomial      24
Tree game      96
Tree of World's moves      10 148 183
Trend      338
Turing, Alan M. (1912—1954) universal computing machine      48
Ultrafilter      283
Ultrafilter nontrivial      283
Upper boundary      136
Upper price      12 151
Upper price strong      328
Upper price weak      328
Upper probability      15
Upper variance      14 80 152
Value at Risk      373
Varadhan, S. R. Sriniva (born 1940) weak solution      347
Variable      66
Variable for market protocol      319
Variable game-theoretic definition      10
Variable indicator      15
Variable partial      149
Variable unbounded forecasting      81
Variance accumulated      153
Variance derivative      202
Variance game-theoretic      14 152
Variance lower      14 152
Variance measure-theoretic      42
Variance of diffusion process      206
Variance upper      14 152
Variation exponent      211
Variation exponent continuous-time      274
Variation exponent relative      275
Variation quadratic      91 176
Variation quadratic game-theoretic      118
Variation quadratic relative      275
Variation quadratic spectrum      209
Variation quadratic spectrum continuous-time      274
Variation quadratic spectrum relative      275
Variation spectrum relative      259
Variation strong      289
Venn, John (1834—1923) probability=frequency      34
Ville, Jean (1910—1988) collectives      48
Ville, Jean (1910—1988) counterexample      18
Ville, Jean (1910—1988) Etude critique de la notion de collectif      198
Ville, Jean (1910—1988) gambling systems      60
Ville, Jean (1910—1988) iterated logarithm      104
Ville, Jean (1910—1988) life and times      197
Ville, Jean (1910—1988) martingales      52
Ville, Jean (1910—1988) minimax theorem      198
Ville, Jean (1910—1988) photograph      1 197
Ville, Jean (1910—1988), Ville's theorem      52 194
VIX      230
Volatility historic      229
Volatility historic implied      229
Volatility historic stochastic      230
Volatility of diffusion process      206
Volatility surface      230
Von Mises, Richard (1883—1957) collectives      46
Von Mises, Richard (1883—1957) debate with Doob      45
Von Mises, Richard (1883—1957) frequentism      18
Von Mises, Richard (1883—1957) gambling systems      60
Von Mises, Richard (1883—1957) in opposition to Kolmogorov      45
Von Mises, Richard (1883—1957) interpretation of probability      43
Von Mises, Richard (1883—1957) Kolmogorov's agreement      50
Von Mises, Richard (1883—1957) life and times      46
Von Mises, Richard (1883—1957) photograph      46
Von Mises, Richard (1883—1957) resistance to Ville's example      49
Von Neumann, John (1903—1957) minimax theorem      97 198
Von Neumann, John (1903—1957) photograph      190
Von Neumann, John (1903—1957) quantum mechanics      189
Von Plato, Jan (born 1951) modern probability      35
Vorst, Ton C. F. (born 1952) discrete hedging      258
Wald, Abraham (1902—1950) collectives      47
Wald, Abraham (1902—1950) Menger's seminar      197
Walley, Peter upper and lower price      59
Weak price      328
Weak upper price      328
Weather derivative      303 306
Weather forecasting      21 162
Whaley, Robert E. (born 1953) implied volatility      230
Wiener, Norbert (1894—1964) Brownian motion      205
Wiener, Norbert (1894—1964) photograph      204
Wiener, Norbert (1894—1964), Wiener process      205
Williams, Peter M. (born 1944) upper and lower price      59
Willinger, Walter (born 1956) dynamic hedging without probabilities      281 349
Willinger, Walter (born 1956) pathwise stochastic integration      349
Wilmott, Paul (born 1959) discrete hedging      258
Witness      83 173
Wolfe, Philip (born 1927) determinate games      97
World divided into Forecaster and Reality      90
World divided into several players      7
World move space      183
World name for Player II      4
Zahle, Martina (born 1950) pathwise stochastic integration      349
Zermelo, Ernst (1871—1853) determinate games      94
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