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| Fleming W.H., Soner H.M. — Controlled Markov Processes and Viscosity Solutions |
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| Предметный указатель |
Adapted processes 403
Adjoint variable 20 115
Admissible control system 135
Admissible control system, discrete time 322
Admissible control system, infinite horizon 139
Admissible controls 153 350
Approximation by value iteration 323
Approximation in policy space 324
Arbitrage 361
Arbitrage, no arbitrage interval 365
Backward evolution equation 122b
Backward evolution operator 121
Barles — Perthame procedure 265
Black — Scholes equation 362
BOND 347
Borel  -algebra 120
Boundary condition, lateral 271
Boundary condition, terminal 269
Boundary cost 7
Boundary, lateral 6
Boundary, terminal 6
Brownian motion 128
Budget constraint 351
Calculus of variations 4 33 37
Cauchy data 34 133
Certainty-equivalent expectation 228
Chapman — Kolmogrov equation 121
Characteristic differential equations 34
Classical solution 65 68 134
Classical solution, infinite horizon 139
Classical solution, singular control 299
Coercivity 33
Comparison, first order equations 89 114
Comparison, second order equations 219 223
Comparison, weak 272
Conjugate points 35 45
Consumption-investment problem 30 168 348
Contingent claim 360
Continuity of the value function, deterministic 99 104
Continuity of the value function, state constraint 114
Continuity of the value function, stochastic control 178 205
Control 5
Control problem, exit time 6
Control problem, infinite horizon 25
Control problem, singular control 296
Control problem, singular control with finite fuel 317
Control problem, state constraint 7 106
Control space 5 130
Control,  -optimal 10
Control, admissible at x 350
Control, optimal 8
Corlor process 135
Covariance matrix 127
Crandall — Ishii lemma 216
Demand process 142
Derivative financial instrument 360
Deterministic evolution 125
Difference quotient, first order 182 326
Difference quotient, second order 182 326
Differentiable function 18
Differential game 377
Differential game, lower game value 382
Differential game, upper game value 381
Diffusion approximation 129
Diffusion process 127
Discount factory 25 123
Discounted cost 25 123
Dissipation inequality 246
Disturbance 245
Drift 127
Duality formula 34 398
Dynamic programming equation, abstract 65
Dynamic programming equation, controlled Markov processes 132 209
Dynamic programming equation, deterministic 12
Dynamic programming equation, deterministic infinite horizon 26 106
Dynamic programming equation, diffusion processes 155
Dynamic programming equation, diffusion processes with infinite horizon 165
Dynamic programming principle, abstract 65
Dynamic programming principle, controlled Markov processes 132 200
Dynamic programming principle, deterministic 11
Dynamic programming principle, differential games 382
Dynamic programming principle, diffusion processes 176 200
Dynkin’s formula 122 399
Elliott — Kalton value 381
Elliptic operators, degenerate 128
Elliptic operators, uniformly 128
Euler equations 35 40 43
Existence theorems 51 52
Exit, probability 244 282
Exit, problem 244
Exit, time 6 153 238
Extremal 35
Feedback control 17
Feedback control, optimal 17
Feller processes 146
Feynman — Kac formula 407
Financial market model 347
Finite difference approximations 324
Finite difference approximations, convergence 331 336
Generalized derivatives 191
Generalized solution 20 193
Generalized solution, , subsolution 193
Girsanov theorem 164 231
H-infinity norm 245
Hamilton — Jacobi — Bellman (HJB) equation, degenerate elliptic 166
Hamilton — Jacobi — Bellman (HJB) equation, degenerate parabolic 156
Hamilton — Jacobi — Bellman (HJB) equation, first order 12 34 48
Hamilton — Jacobi — Bellman (HJB) equation, second order 156
Hamilton — Jacobi — Bellman (HJB) equation, uniformly elliptic 165
Hamilton — Jacobi — Bellman (HJB) equation, uniformly parabolic 156
Hamiltonian 12
HARA function 30 169 356
harmonic oscillator 3
Homogenization 292
Infinite horizon 25 134 164
Infinitesimal generator 65
Inventory level 3
Isaacs, lower PDE 379
Isaacs, minimax condition 379
Isaacs, upper PDE 378
Jacobi conditions 35
Jump Markov processes 127
Jump rate 264
Lagrange form 38 131
Large deviations 244 278
Large deviations for exit probabilities 282
Levy form 127
Linear quadratic regulator, deterministic 4 13
Linear quadratic regulator, discounted 141
Linear quadratic regulator, exponential-of-quadratic 254
Linear quadratic regulator, indefinite sign 237
Linear quadratic regulator, stochastic 136 237
Lipschitz continuous 19
Lipschitz continuous, locally 19
| Local time 307
Logarithmic transformation 227
Logarithmic transformation for Markov diffusions 237
Logarithmic transformation for Markov processes 255
Markov chain 125
Markov control policy 17 130 159
Markov control policy, discrete time 177
Markov control policy, optimal 17 136 160
Markov control policy, stationary 167
Markov diffusion processes 127
Markov processes 120
Markov processes, autonomous 123
Maslov idempotent probability 242
Max-plus addition 242
Max-plus addition, expectation 242
Max-plus addition, multiplication 242
Max-plus addition, stochastic control 390
Mayer form 131
Mean average action 138
Mean exit time (minimum) 167
Merton’s portfolio problem 168 348
Merton’s portfolio problem, with random parameters 368
Minimal super-replicating cost 368
Mollification 402
Nisio semigroup 146
Numerical cutoffs 343
Numerical schemes, explicit 327 331
Numerical schemes, implicit 327 331
Optimal trajectory 20 45
Option, call 360
Option, digital 361
Option, put 361
Parabolic operators, degenerate 128
Parabolic operators, uniformly 128
Parameter process 126
Picard iteration 297
Piecewise deterministic process 127
Point of differentiability 18 85
Poisson process 59
Pontryagin maximum principle 20 115
Portfolio, constraints 366
Portfolio, selection problem 168 348 368
Portfolio, transaction costs 354
Post jump location 264
Principle of smooth fit 306
Processes of bounded variations 296
Production planning 2 32 142
Production rate 2 142
Progressively measurable, controls 153
Progressively measurable, processes 153 403
Rademacher theorem 19
Random evolution 126
Reachability 7
Reaction-diffusion equation 292
Reference probability system 154
Reflected brownian motion 307 309
Regular point 42
Ricatti equation 15 137 255
Risk neutral probability 350
Risk sensitive control 250
Risk sensitive control, limit game 337
Risk, averting 230
Risk, neutral 229
Risk, seeking 230
Risk, sensitivity 228
Running cost 3 6 123 131
Schrodinger’s equation 243
Semiclassical limit 243
Semiconcave function 87 190 214
Semicontinuous envelope, lower 267
Semicontinuous envelope, upper 267
Semiconvex function 87 214
Semigroup 62
Semilinear equations 162 195
Singular control 293
Small noise limit 239 282 389
State constraint 7 106
State space 120 130
Static games 376
Stochastic differential equations 128 152 403
Stochastic mechanics 137
Stochastic volatility 369
Stock 347
Storage function 246
Storage function, minimal 247
Strategy, progressive 381
Strategy, strictly progressive 392
Strike price 360
Subdifferentials 84
Subdifferentials, of convex analysis 85
Subdifferentials, second order 210
Super-replication 364
Superdifferentials 83
Superdifferentials, second order 210
Terminal cost 3 6 123 131
Test function 65
Time discretization 322 390
Transaction cost 354
Transaction cost, no-transaction region 357
Transition distribution 120
Transversality conditions 21
Uniqueness, discontinuous 114
Uniqueness, first order 89 97
Uniqueness, second order 221 223
Uniqueness, state constraint 114
Utility function 30 168 349
Utility function, HARA 30 169 356
Utility pricing 362
Value function 64 72
Value function, deterministic 9
Value function, differential game 381
Value function, diffusion processes 154
Value function, discrete 322
Vanishing viscosity 280
Verification Theorem, controlled Markov processes 134
Verification Theorem, controlled Markov processes with infinite horizon 140
Verification Theorem, deterministic 13 16 27
Verification Theorem, differential games 380
Verification Theorem, diffusion processes 157
Verification Theorem, diffusion processes with infinite horizon 166
Verification Theorem, risk sensitive control 254
Verification Theorem, singular control 300
Viscosity solutions, boundary conditions 271
Viscosity solutions, constrained 109
Viscosity solutions, definition 68 70
Viscosity solutions, discontinuous 266
Viscosity solutions, first order equations 83
Viscosity solutions, infinite horizon 106
Viscosity solutions, second order equations 70
Viscosity solutions, singular control 311
Viscosity solutions, stability 76 77 268
Viscosity solutions, state constraint 107
weakly convergent sequence 50
White noise 129
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