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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
$\sigma$-algebra      40
Accumulated variance      153
Adapted      169
Algebra of sets      40 291
Almost sure price      344
Almost surely game-theoretic meaning      17 61 82 90
Almost surely in probability protocol      187
Almost surely measure-theoretic meaning      61
American option      217 317
Anderson, Oskar      1887—1960
Anderson, Oskar Cournot's bridge      44
Anderson, Robert M. (born 1951) measure on internal functions      291
Approximation theorem      139
Arbitrage portfolio      355
Arbitrage-free      233
At-the-money      264
Axiom of Dependent Choice      98
Axiom of determinacy      97
Bachelier, Louis      1870—1946
Bachelier, Louis behavior of stock-market prices      203
Bachelier, Louis central limit theorem      242
Bachelier, Louis continuous-time protocol      278
Bachelier, Louis continuous-time protocol with jumps      310
Bachelier, Louis discrete-time protocol      240
Bachelier, Louis dynamic hedging      60
Banach space      118
Bankruptcy      218
Basic payoff      110
Bernard, Claude (1813—1878) determinism      35
Bernoulli, Jacob      1654—1705
Bernoulli, Jacob Ars Conjectandi      32
Bernoulli, Jacob, Bernoulli's theorem      33—34 38 124
Bernoulli, Jacob, coin tossing      164
Bernoulli, Jacob, photograph      124
Bernoulli, Jacob, practical certainty      44 60
Bernoulli, Jacob, used Fermat's and Pascal's methods      32
Bernoulli, Nicholas (1687—1759) used Fermat's and Pascal's methods      32
Bernstein, Sergei (1880—1968) dependent variables      54
Bernstein, Sergei (1880—1968) revival of probability      35
Bertoin, Jean (born 1961) Ito's lemma      349
Bertrand, Joseph (1822—1900) gambling systems      49 55
Bick, Avi (born 1947) dynamic hedging without probabilities      281 349
Bid-ask spread      188
Binary possibility      24 63
Binomial distribution      165
Binomial tree      24
Black — Scholes equation      221 224
Black — Scholes formula continuous-time      279
Black — Scholes formula diffusion      344—345
Black — Scholes formula discrete-time      249
Black — Scholes formula game-theoretic      224
Black — Scholes formula publication      215
Black — Scholes formula square      300
Black — Scholes formula stochastic      221
Black — Scholes formula with constrained variation      249
Black — Scholes formula with informal constraints      223
Black — Scholes formula with interest      294
Black — Scholes model      25
Black — Scholes protocol basic      217
Black, Fischer (1938—1995) photograph      216
Black, Fischer (1938—1995), Black — Scholes formula      215
Blackwell game      97
Bodie, Zvi (born 1943) insuring long-run stock returns      371
Boltzmann, Ludwig (1844—1906) statistical physics      35
Borel, Emile (1871—1956), Borel $\sigma$-algebra      41
Borel, Emile (1871—1956), Borel set      41
Borel, Emile (1871—1956), Borel — Cantelli — Levy lemma      88
Borel, Emile (1871—1956), continuous probability      37
Borel, Emile (1871—1956), discussion with Reichenbach      57
Borel, Emile (1871—1956), measure theory      36
Borel, Emile (1871—1956), photograph      37
Borel, Emile (1871—1956), quasi-Borel set      96
Borel, Emile (1871—1956), resistance to Kolmogorov's framework      42
Borel, Emile (1871—1956), revival of probability      35
Borel, Emile (1871—1956), strong law      38 118
Boundary      136
Bounded forecasting      70
Bounded forecasting, bounded-variance      161
Bounded forecasting, constant-variance      159
Bounded forecasting, finite-horizon      125 141
Bounded forecasting, fixed-variance      160
Bounded forecasting, zero forecasts      65
Bounded variation      274
Bounding capital process      82
Bounding strategy      82
Box dimension      211
Boyle, Phelim P. (born 1941) discrete hedging      258
Brier, Glenn W. (1913-circa 1999) weather forecasting      57
Britten-Jones, Mark remaining variance      349
Brownian motion      205
Brownian motion definition      206
Brownian motion fractional      212 290
Brownian motion geometric      25 207
Calibration      162
Calvet, Laurent observed variation spectra      253
Can buy and can sell      12
Can force      65 187
Cantelli, Francesco (1875—1972) Borel — Cantelli — Levy lemma      88
Cantelli, Francesco (1875—1972) revival of probability      35
Capital process      150
Capital process bounding      82
Caratheodory, Constantin(1873—1950) extension theorem      195 291
Caratheodory, Constantin(1873—1950) Menger's seminar      197
Cauchy, Augustin Louis (1789—1857) stable laws      311
Central limit theorem Bachelier's      242
Central limit theorem De Moivre's      33 127
Central limit theorem dependent variables      54
Central limit theorem history      164
Central limit theorem Laplace's      34
Central limit theorem Lindeberg's      153
Central limit theorem Lyapunov's      162
Central limit theorem name coined by Polya      165
Central limit theorem one-sided      133
Central limit theorem one-sided for securities market      365
Certainty      32
Chance      34
Characteristic function      311
Chebyshev, Pafnutii L. (1821—1894) central limit theorem      165
Chebyshev, Pafnutii L. (1821—1894) revival of probability      35
Chicago Board Options Exchange LEAPS      252
Chicago Board Options Exchange VIX      230
Church, Alonzo (1903—1995) Closing Market      353
Church, Alonzo (1903—1995) collectives      47
Closure      136
Coherence      14 150 186
Coherence for market      322
coin tossing      177
Collateral duties      65 78
Collective      43 46
Compensator      85
Complement      79
Complete stopping time      117
Comte, Auguste (1798—1857) determinism      35
Conditional expectation      42 169
Conditional expected value      71
Conditional probability      40
Conditional probability game-theoretic interpretation      179
Conditional probability notation      41
Continuation region      135
Continuous nonstandard function      273 286
Continuous probability      35 42
Continuum Hypothesis      284
Conventionalism      37
Converge in probability      152
Copeland Sr., Arthur H.(1898—1970) collectives      47
Corners      136
Cost      12
Countable additivity      41
Countable saturation      291
Cournot's bridge      44
Cournot, Antoine Augustin (1801—1877) Cournot's bridge      44—45 56 60
Cournot, Antoine Augustin (1801—1877) gambling systems      49 55
Cournot, Antoine Augustin (1801—1877) photograph      44
Cournot, Antoine Augustin (1801—1877) probability and chance      34
Covariates      192
Cox, David R. (born 1924) photograph      192
Cox, David R. (born 1924) regression model      191
Cramer, Harald (1893—1985) advocated Kolmogorov's framework      39
Crepel, Pierre (born (1947) interview of Ville      197
Cross-variation      258
Cut      183
Cutland, Nigel J. (born 1944) Anderson's construction      292
Dambis, K.E. change of time      306
Davis, Morton determinate games      97
Dawid, A. Philip (born 1946) iterated logarithm      104
Dawid, A. Philip (born 1946) photograph      163
Dawid, A. Philip (born 1946) prequential principle      8
Dawid, A. Philip (born 1946) probability forecasting      58 164
De Finetti, Bruno (1906—1985) conditional probability      42
De Finetti, Bruno (1906—1985) emphasis on price      60
De Finetti, Bruno (1906—1985) infinitely divisible laws      312
De Finetti, Bruno (1906—1985) neosubjectivism      5
De Finetti, Bruno (1906—1985) neosubjectivists      59
De Finetti, Bruno (1906—1985) opposition to Kolmogorov      45
De Finetti, Bruno (1906—1985) photograph      59
De Moivre, Abraham (1667—1754) coin tossing      126 164
De Moivre, Abraham (1667—1754) De Moivre's theorem      33 127
De Moivre, Abraham (1667—1754) photograph      127
De Moivre, Abraham (1667—1754) sharpened Bernoulli's theorem      33
De Moivre, Abraham (1667—1754) used Fermat's and Pascal's methods      32
Decision analysis      21
Delta      221
Derivative security      216
Derivative security strictly convex      302
Derivative security variance derivative      202
Determinism      33—34
Diffusion as continuous Levy process      316
Diffusion equation      129 221
Diffusion game-theoretic process      338
Diffusion process      206
Diffusion protocol      337—338
Diffusion term (for semimartingale)      315
Doeblin, Wolfgang      1915—1940
Doeblin, Wolfgang seminar with Ville      198
Doob, Joseph L. (born 1910) advocated Kolmogorov's framework      39
Doob, Joseph L. (born 1910) debate with von Mises      45
Doob, Joseph L. (born 1910) defined martingale      55
Doob, Joseph L. (born 1910) gambling systems      55
Doob, Joseph L. (born 1910) inequality      56 196
Doob, Joseph L. (born 1910) martingale convergence theorem      81 84 172
Doob, Joseph L. (born 1910) measure-theoretic martingales      54
Doob, Joseph L. (born 1910) photograph      45 134
Doob, Joseph L. (born 1910) reviewed Ville's book      54
Dot product      353
Drift diffusion process      206
Drift term (for semimartingale)      315
Dubins, Lester E. (born 1927) change of time      306
Dubins, Lester E. (born 1927) conservation of fairness      56
Dynamic hedging      2 4
Earlier notation for conditional probability $(P_{A}(B))$      41
Edwards, A.W.F (born 1935) work on Pascal      32
Efficient markets      228
Efficient score      194
Efficient-market hypothesis      6 351
Efficient-market hypothesis game-theoretic nature      228
Efficient-market hypothesis many tests      351
Efficient-market hypothesis value at risk      373
Efficient-market hypothesis with options      371
Efficient-markets hypothesis      6 229
Einstein, Albert      1879—1955
Einstein, Albert, Brownian motion      204
Emanuel, David discrete hedging      258
Empirical volatility      368
Empiricism      34
Equivalent martingale measure      348
Equivalent portfolios      355
European call      216
European option      216
Event      40 67 90 169
Event game-theoretic definition      11
Event unbounded forecasting      81
Exercise region      135
Expected value      14 42
Experiment      40
External object      291
Faber, Georg (1877—1966) proof of Borel's strong law      38
Failure model      192
Fair-coin game      64
Feller, William (1906—1970) advocated Kolmogorov's framework      39
Feller, William (1906—1970) iterated logarithm      119
Feller, William (1906—1970) Lindeberg's theorem      166
Fermat, Pierre de (1601—1665) correspondence with Pascal      30
Field of sets      40
Filter      283
Filtered measurable space      169
Filtered probability space      169
Filtration      169
Financial instrument      321
Financial instrument passive      322
finite      284
Fisher, Adlai (born 1969) observed variation spectra      253
Folk stochasticism      21
Follmer, Hans (born 1941) pathwise integral      349
Follows game-theoretic differential equation      338
Forcing      65
Forcing in probability protocol      90 187
Forcing in unbounded forecasting      79
Forcing weak      68
Forecaster as part of World      7
Forecaster move space      90
Forecasting game bounded      65
Forecasting game unbounded      77
Forecasting protocol bounded and finite-horizon      133
Forecasting protocol predictably unbounded      102
Forecasting protocol simplified predictably unbounded      103
Forecasting protocol unbounded      79
Forecasting protocol unbounded upper      89
Fourier, Joseph B. (1768—1830) heat equation      129
Fourier, Joseph B. (1768—1830) photograph      129
Fractional Brownian motion      212 290
Frechet, Maurice (1878—1973) advocated Kolmogorov's framework      39
Frechet, Maurice (1878—1973) gambling systems      55
Frechet, Maurice (1878—1973) Geneva contribution      39 45
Frechet, Maurice (1878—1973) measure theory      36
Frequency Jacob Bernoulli      33
Frequency nineteenth century      34
Frequency relative      18
Frequency Richard von Mises      46
Frequentism Kolmogorov's      43
Frequentism von Mises's      46
Function market      332
Function nonstandard      273
Function regulated      290
Function smooth      127
Function standard      273
Function strictly convex      302
Function submarket      332
Function supermarket      331
Function superparabolic      137
Function superparabolic smooth      139
Fundamental interpretative hypothesis      5 14
Fundamental interpretative hypothesis finitary      15
Fundamental interpretative hypothesis in Kolmogorov      43
Fundamental interpretative hypothesis infinitary      15
Fundamental interpretative hypothesis outside mathematics      62
Gain function      150 183
Gain function constant      90
Gain process      152
Gale, David determinate games      97
Gambling protocol compared with market protocol      319
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