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Fleming W.H., Soner H.M. — Controlled Markov Processes and Viscosity Solutions
Fleming W.H., Soner H.M. — Controlled Markov Processes and Viscosity Solutions

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Название: Controlled Markov Processes and Viscosity Solutions

Авторы: Fleming W.H., Soner H.M.

Аннотация:

This book is intended as an introduction to optimal stochastic control for continuous time Markov processes and to the theory of viscosity solutions. Stochastic control problems are treated using the dynamic programming approach. The authors approach stochastic control problems by the method of dynamic programming.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second Edition

Год издания: 2005

Количество страниц: 448

Добавлена в каталог: 08.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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 $\sigma$-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, $\delta$-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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