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| Malliaris A.G., Brock W.A. — Stochastic methods in economics and finance |
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| Предметный указатель |
 -algebra 2
-field 2
-finite measure 12
Absolute risk aversion 191 227
Absolutely continuous measure 12
Absorbing barrier 199
Absorbing states 107
Adjustment-cost model 157
Admissible process 183
Alchian, A. 61
Almost everywhere (a.e.) 9
Almost surely (a.s.) 9
Anderson, B. 139
Anticipated price process 158
Antosiewicz, H. 136
Aoki, M. 132 139
Araujo, A. 139
Arbitrage theory of capital asset pricing 242 277
Archer, S.H. 237 277
Arnold, L. 70 72 74 75 77 79 80 81 96 99 100 102 133
Arrow — Debreu model 247 277
Arrow, K.J. 108 138 217
Ash, R.B. 3 10 11 12 29 32 60 61
Astrom, K.J. 66 67 70 132 133 139
Athans, M. 139
Auto-covariance function 128
Average cost 191
Axiom of expextation formation 28
Bachelier, L. 61
Backward differences 129
Backwards heat equation 126
Balakrishman, A.V. 132
Baron, D. 214
Batra, R.N. 214
Baumol, W.J. 238
Bayes’ Theorem 59
Bcwlcy.T. 184 215
Bellman, R. 108 139
Bellman’s principle of optimality 108 115 148
Benes, U.E. 139
Benveniste, L. 139 186 249 251
Berkowitz, L.D. 139
Bernoulli, D. 62
Bertsekas, D.P 132 139
Bharucha-Reid, A.T. 62 70 72
Bicksler, J.L. 272
Billingsley, P. 5 13 15 16 19 29 32 34 37 58 60 61 62
Binomial distribution 6
Bismut approach to optimal stochastic control 118—121 125 150—152
Bismut, J.M. 115 118 119 120 139 150 160 163 214 215
Black, F. 220 221 222 233 273 276
Black-Scholcs option pricing model 220—223 268 273—275
Boole’s inequality 58
Borel sets 2 57
Borel — Cantelli lemma 4 93
Borg, G. 136
Boundedness property of solutions 104
Bourguignon, F. 106 141 214
Boyce, W.M. 216
Brainard, W. 192 216
Breeden, D.T. 275
Breiman, L. 63
Brennan, J.J. 276
Brock, W.A. 53 138 139 140 167 168 182 185 187 188 205 214 215 216 251 277
Brownian motion process 36—38 61—62
Brownian motion process, geometric 38 (see also “Wiener process”)
Bryson, A.E. 139
Bucy, R.S. 136
Burmeistcr, E. 142
Capital asset pricing model 182 237 245—253 275—277
Capital market efficiency 23 61 234
Cass, D. 139
Certainty equivalence 193 256—262
Cesari, L. 136
Chapman — Kolmogorov equation 40—41
Chebyshev’s inequality 58
Chow, Y.S. 45 51 52 53 63 216
Chow.G.C 67 132
Chung, K.L. 60
Cinlar, E. 62 63
Competitive process 161—168
Complete probability space 3 161
Condition, of compatability 34
Condition, of no arbitrage profits 263
Condition, of symmetry 33—34
Conditional distribution 16
Conditional expectation 14 22 28 59
Conditional expected rate of return 27—28
Conditional expected value 14
Conditional mean 67
Conditional probability 12—13
Consistency properties 33
Constant relative risk aversion 24 174 191
Constantinides, G.M. 236 237 238 270 276 277
Consumer surplus 159
Continuation region 126 194
Continuous in the mean square 128
Continuous parameter process 32
Contraction mapping theorem 255
control variable 108
Convergence, almost sure 167—168
Convergence, dominated 10 59
Convergence, in distribution 8 185 188
Convergence, in probability 7 76—77
Convergence, in the mean square 77
Convergence, monotone 10 59
Convergence, with probability one 7
Convertible bond 274
Cornell, B. 62
Correlation coefficient 11 192 232
Costatc variable 110
Counting measure 57
Covariance 11 246
Covariance function 1 28
Cox, D.R. 62 200
Cox, J.C 273 274 276 277
Crane, D.B. 277
Daellenbach, H.G. 277
Danthine, J.P. 62
Davis, M.H.A. 139
Debt 273
Decomposition 8
DeGroot, M. 45 47 48 49 51 63
Dellacherie, C 61 139
Demand function, linear in wealth 228
Demand function, random 207
Density function 6 189
Diamond, P.A. 214
Differential operator 100
Differentiate in the mean square 98
Diffusion process 99
Diffusion process, coefficient 99 108
Diffusion process, property 99—100 145
Directly testable equations 262—263
Discount on future utility 108
Discrete parameter process 32
Distribution, binomial 6
Distribution, common 43 183
Distribution, initial 40
Distribution, joint 5 53
Distribution, marginal 5
Distribution, normal 6
Distribution, of a random variable 5 189
Distribution, Poisson 6
Distribution, stationary 40 106—108 146—147
Distribution, steady state 40 106—108
Disturbances, additive 192
Disturbances, multiplicative 192—193
Dobell, A.R. 142
Dominated Convergence Theorem 10 59
| Dominated measure 12
Doob, J.L. 19 29 61 62 69 133 139
Dothan, L.U. 276
Dreyfus, S.E. 139
Drift 38 99 108
Dvoretzky, A. 63
Dynamic deterministic model 66—67
Dynkin, E.B. 62 63
Edgeworth box 208
Elastic random walk 270
Environmental factor 119
Eppcn, G.D. 277
Equilibrium 102 243
Equilibrium distribution 106—108
Equilibrium solution 102 206
Equilibrium, stable 103 137 206
equity 273
European put 273
Event 2
Excessive function 126
Exercise price 222
Expectation 8
Expected present discounted value 24
Exponentially stable in the mean 137
Extended integrand problem 170
Fair game 17 261
Falb, P.L. 139
Fama, E. 18 22 23 61 62 275 277
Fatou’s theorem 10 59
Feller, W. 61 62 105 106 138
Fermat, P. 61
Final gain 125
Finite decomposition 8
Finite-dimensional distributions 33
Fischer, S. 217 230 232 276
Fixed point problem 254
Fleming, W.H. 108 139
Foldes, L. 29 214
Forsythe, R. 214
Francis, J.C. 237
Free boundary 126
Free boundary problem 124—128
Frenkcl, J.A. 239 240 241
Friedman, A. 78 132 235
Friedman, M. 59
Fundamental partial differential equation of optimal stopping 196
Fundamental theorem of calculus for Ito’s stochastic integral 91—92
Furopean call 273
Futures pricing 21
Gale, D. 251
Gal’perin, E.A. 139
Game, fair 17 261
Game, favorable 17
Game, unfavorable 17
Generalized hamiltonian 165
Generalized martingale 19
Generated -field 2
Gertler, M. 182 216
Gihman — Skorohod approach to stability 103
Gihman, J 62 70 72 77 79 81 93 94 96 97 98 101 103 104 122 132 135
Global asymptotically stable 105
Global solution 94
Gould, J.P. 214
Grossman, S. 61
Growth under uncertainty, monetary 206
Growth under uncertainty, N-sector model of 182—188
Growth under uncertainty, open economy 143—144
Growth under uncertainty, optimal saving function 148
Growth under uncertainty, properties of 144—146
Growth under uncertainty, stationary distribution of 146—148
Growth under uncertainty, steady state per capita output 147
Growth under uncertainty, stochastic differential equation ot 142—143
Hadjimichalakis, M. 206
Hadley, G. 139
Hahn, W. 136
Hakansson, N.H. 275
Hale, J. 139
Hall, R.E. 28 29 61
Hamilton — Jacobi — Bellman equation of stochastic control theory 110 114 148 172 209
Harrison, J.M. 62 80 275
Hartman, P. 136 139
Heat equation 126
Helpman, E. 214
Hestenes, M. 139
Hilbert-valucd processes 133
Ho, Y. 139
Hoel, P.G. 40 62
Houthakker, H. 61
Humphrey, T.M. 276
Hyperbolic absolute risk-aversion unility functions 226—228
Inaccessible 107
Independent events 4
Independent random variable 6
Index bond, as a hedge against inflation 233
Index bond, demand for 230—233
Indicator function 46
Inflation, expected rate 152
Inflation, inertia 180
Inflation, stochastic process 180 230
Information sets, semi-strong 22
Information sets, strong 22—23
Information sets, weak 22—24 26
Ingersoll, J.E. 273 274 276 277
Initial distribution 40
Integrability property 18
Integrable 9 18
Integrable stochastic sequence 51—52
Integral equation 69
Interest rate process 233—234
International monetary model under uncertainty 211
Intertemporal stochastic optimization 28
Intrilligator, M.D 132
Investment-output plan 158
Ishii, Y. 214
Ito, K. 37 69 81 132 133 135
Ito’s lemma 80—92 95 122—123 130 142 144 146 175 180 208—209 218 224 234 237 272
Ito’s stochastic differential equation 68 92—96 133 142—143 180 217 219 220—221 223 227 230 234 236 239 268—270
Ito’s stochastic integral 74 76 78 133—135
Jensen, M.C. 23 24
Jensen’s Inequality 15 30 58
Jovanovic, B. 216 239 240 241
Jump process 121—124 139 209 228—230
Kantor, B. 214
Karlin, S. 61 62
Kats, I.I. 136
Khas’minskii, R.Z. 106 138
Kolmogorov, A.N. 61 62
Kolmogorov’s backward equation 101
Kolmogorov’s inequality 30
Kolmogorov’s theorem 34
Kozin, F. 131 137 138
Krasovskii, N.N. 136. 139
Krcps, D.M. 275
Kunita, H. 133
Kurz, M. 108 138
Kushner, H.J. 104 105 122 136 137 139 140
Kussmaul, A.V. 133
Kwakernaak, H. 139
Lack of memory 36
Ladde, G.S. 70 72 81 106
Lakshmikantham, V. 70 72 81.
Laplace transform 198
LaSalle, J.P. 136
Lau, M. 214
Law of a random variable 5
Learning without forgetting 18
Lebesgue integral 9 73
Lebesgue measure 3
Lee, E.B. 139
Lefschetz, S. 136 139
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