Sequential stochastic optimization [[electronic resource] /] / R. Cairoli, Robert C. Dalang
| Sequential stochastic optimization [[electronic resource] /] / R. Cairoli, Robert C. Dalang |
| Autore | Cairoli R (Renzo), <1931-1994.> |
| Pubbl/distr/stampa | New York, : J. Wiley & Sons, c1996 |
| Descrizione fisica | 1 online resource (348 p.) |
| Disciplina | 519.7 |
| Altri autori (Persone) | DalangRobert C. <1961-> |
| Collana | Wiley series in probability and mathematical statistics |
| Soggetto topico |
Optimal stopping (Mathematical statistics)
Dynamic programming Stochastic control theory |
| ISBN |
1-283-22799-1
9786613227997 1-118-16439-3 1-118-16440-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Sequential Stochastic Optimization; Contents; Preface; Notation and Conventions; 1. Preliminaries; 1.1 Filtered Probability Spaces; 1.2 Random Variables; 1.3 Stopping Points; 1.4 Increasing Paths and Accessible Stopping Points; 1.5 Some Operations on Accessible Stopping Points; 1.6 Stochastic Processes and Martingales; Exercises; Historical Notes; 2. Sums of Independent Random Variables; 2.1 Maximal Inequalities; 2.2 Integrability Criteria for the Supremum; 2.3 The Strong Law of Large Numbers; 2.4 Case Where the Random Variables Are Identically Distributed; Exercises; Historical Notes
3. Optimal Stopping3.1 Stating the Problem; 3.2 Snell's Envelope; 3.3 Solving the Problem; 3.4 A Related Problem; 3.5 Maximal Accessible Stopping Points; 3.6 Case Where the Index Set is Finite; 3.7 An Application to Normalized Partial Sums; 3.8 Complements; Exercises; Historical Notes; 4. Reduction to a Single Dimension; 4.1 Linear Representation of Accessible Stopping Points; 4.2 Applications; 4.3 Linear Representation in the Setting of Inaccessible Stopping Points; Exercises; Historical Notes; 5. Accessibility and Filtration Structure; 5.1 Conditions for Accessibility 5.2 Consequences for the Structure of the Filtration5.3 The Bidimensional Case; 5.4 Predictability of Optional Increasing Paths; 5.5 The Combinatorial Structure of a Filtration; 5.6 The Combinatorial Structure of a Filtration Satisfying COl; 5.7 Optimal Stopping and Linear Optimization; Exercises; Historical Notes; 6. Sequential Sampling; 6.1 Stating the Problem; 6.2 Constructing the Model; 6.3 The Reward Process and Snell's Envelope; 6.4 Describing the Optimal Strategy; 6.5 The Likelihood-Ratio Test; 6.6 Applications; 6.7 Complement; Exercises; Historical Notes; 7. Optimal Sequential Control 7.1 An Example7.2 Preliminaries; 7.3 Controls; 7.4 Optimization; 7.5 Optimization Over Finite Controls; 7.6 Case Where the Index Set Is Finite; 7.7 Extension to General Index Sets; Exercises; Historical Notes; 8. Multiarmed Bandits; 8.1 Formulating the Problem; 8.2 Index Controls; 8.3 Gittins Indices; 8.4 Characterizing Optimal Controls; 8.5 Examples; Exercises; Historical Notes; 9. The Markovian Case; 9.1 Markov Chains and Superharmonic Functions; 9.2 Optimal Control of a Markov Chain; 9.3 The Special Case of a Random Walk 9.4 Control and Stopping at the Time of First Visit to a Set of States9.5 Markov Structures; Exercises; Historical Notes; 10. Optimal Switching Between Two Random Walks; 10.1 Formulating and Solving the Problem; 10.2 Some Properties of the Solution; 10.3 The Structure of the Solution; 10.4 Constructing the Switching Curves; 10.5 Characterizing the Type of the Solution; 10.6 Determining the Type of the Solution; Exercises; Historical Notes; Bibliography; Index of Notation; Index of Terms |
| Record Nr. | UNINA-9910139611903321 |
Cairoli R (Renzo), <1931-1994.>
|
||
| New York, : J. Wiley & Sons, c1996 | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Sequential stochastic optimization [[electronic resource] /] / R. Cairoli, Robert C. Dalang
| Sequential stochastic optimization [[electronic resource] /] / R. Cairoli, Robert C. Dalang |
| Autore | Cairoli R (Renzo), <1931-1994.> |
| Pubbl/distr/stampa | New York, : J. Wiley & Sons, c1996 |
| Descrizione fisica | 1 online resource (348 p.) |
| Disciplina | 519.7 |
| Altri autori (Persone) | DalangRobert C. <1961-> |
| Collana | Wiley series in probability and mathematical statistics |
| Soggetto topico |
Optimal stopping (Mathematical statistics)
Dynamic programming Stochastic control theory |
| ISBN |
1-283-22799-1
9786613227997 1-118-16439-3 1-118-16440-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Sequential Stochastic Optimization; Contents; Preface; Notation and Conventions; 1. Preliminaries; 1.1 Filtered Probability Spaces; 1.2 Random Variables; 1.3 Stopping Points; 1.4 Increasing Paths and Accessible Stopping Points; 1.5 Some Operations on Accessible Stopping Points; 1.6 Stochastic Processes and Martingales; Exercises; Historical Notes; 2. Sums of Independent Random Variables; 2.1 Maximal Inequalities; 2.2 Integrability Criteria for the Supremum; 2.3 The Strong Law of Large Numbers; 2.4 Case Where the Random Variables Are Identically Distributed; Exercises; Historical Notes
3. Optimal Stopping3.1 Stating the Problem; 3.2 Snell's Envelope; 3.3 Solving the Problem; 3.4 A Related Problem; 3.5 Maximal Accessible Stopping Points; 3.6 Case Where the Index Set is Finite; 3.7 An Application to Normalized Partial Sums; 3.8 Complements; Exercises; Historical Notes; 4. Reduction to a Single Dimension; 4.1 Linear Representation of Accessible Stopping Points; 4.2 Applications; 4.3 Linear Representation in the Setting of Inaccessible Stopping Points; Exercises; Historical Notes; 5. Accessibility and Filtration Structure; 5.1 Conditions for Accessibility 5.2 Consequences for the Structure of the Filtration5.3 The Bidimensional Case; 5.4 Predictability of Optional Increasing Paths; 5.5 The Combinatorial Structure of a Filtration; 5.6 The Combinatorial Structure of a Filtration Satisfying COl; 5.7 Optimal Stopping and Linear Optimization; Exercises; Historical Notes; 6. Sequential Sampling; 6.1 Stating the Problem; 6.2 Constructing the Model; 6.3 The Reward Process and Snell's Envelope; 6.4 Describing the Optimal Strategy; 6.5 The Likelihood-Ratio Test; 6.6 Applications; 6.7 Complement; Exercises; Historical Notes; 7. Optimal Sequential Control 7.1 An Example7.2 Preliminaries; 7.3 Controls; 7.4 Optimization; 7.5 Optimization Over Finite Controls; 7.6 Case Where the Index Set Is Finite; 7.7 Extension to General Index Sets; Exercises; Historical Notes; 8. Multiarmed Bandits; 8.1 Formulating the Problem; 8.2 Index Controls; 8.3 Gittins Indices; 8.4 Characterizing Optimal Controls; 8.5 Examples; Exercises; Historical Notes; 9. The Markovian Case; 9.1 Markov Chains and Superharmonic Functions; 9.2 Optimal Control of a Markov Chain; 9.3 The Special Case of a Random Walk 9.4 Control and Stopping at the Time of First Visit to a Set of States9.5 Markov Structures; Exercises; Historical Notes; 10. Optimal Switching Between Two Random Walks; 10.1 Formulating and Solving the Problem; 10.2 Some Properties of the Solution; 10.3 The Structure of the Solution; 10.4 Constructing the Switching Curves; 10.5 Characterizing the Type of the Solution; 10.6 Determining the Type of the Solution; Exercises; Historical Notes; Bibliography; Index of Notation; Index of Terms |
| Record Nr. | UNINA-9910831074003321 |
Cairoli R (Renzo), <1931-1994.>
|
||
| New York, : J. Wiley & Sons, c1996 | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Sequential stochastic optimization / / R. Cairoli, Robert C. Dalang
| Sequential stochastic optimization / / R. Cairoli, Robert C. Dalang |
| Autore | Cairoli R (Renzo), <1931-1994.> |
| Pubbl/distr/stampa | New York, : J. Wiley & Sons, c1996 |
| Descrizione fisica | 1 online resource (348 p.) |
| Disciplina | 519.2 |
| Altri autori (Persone) | DalangRobert C. <1961-> |
| Collana | Wiley series in probability and mathematical statistics |
| Soggetto topico |
Optimal stopping (Mathematical statistics)
Dynamic programming Stochastic control theory |
| ISBN |
9786613227997
9781283227995 1283227991 9781118164396 1118164393 9781118164402 1118164407 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Sequential Stochastic Optimization; Contents; Preface; Notation and Conventions; 1. Preliminaries; 1.1 Filtered Probability Spaces; 1.2 Random Variables; 1.3 Stopping Points; 1.4 Increasing Paths and Accessible Stopping Points; 1.5 Some Operations on Accessible Stopping Points; 1.6 Stochastic Processes and Martingales; Exercises; Historical Notes; 2. Sums of Independent Random Variables; 2.1 Maximal Inequalities; 2.2 Integrability Criteria for the Supremum; 2.3 The Strong Law of Large Numbers; 2.4 Case Where the Random Variables Are Identically Distributed; Exercises; Historical Notes
3. Optimal Stopping3.1 Stating the Problem; 3.2 Snell's Envelope; 3.3 Solving the Problem; 3.4 A Related Problem; 3.5 Maximal Accessible Stopping Points; 3.6 Case Where the Index Set is Finite; 3.7 An Application to Normalized Partial Sums; 3.8 Complements; Exercises; Historical Notes; 4. Reduction to a Single Dimension; 4.1 Linear Representation of Accessible Stopping Points; 4.2 Applications; 4.3 Linear Representation in the Setting of Inaccessible Stopping Points; Exercises; Historical Notes; 5. Accessibility and Filtration Structure; 5.1 Conditions for Accessibility 5.2 Consequences for the Structure of the Filtration5.3 The Bidimensional Case; 5.4 Predictability of Optional Increasing Paths; 5.5 The Combinatorial Structure of a Filtration; 5.6 The Combinatorial Structure of a Filtration Satisfying COl; 5.7 Optimal Stopping and Linear Optimization; Exercises; Historical Notes; 6. Sequential Sampling; 6.1 Stating the Problem; 6.2 Constructing the Model; 6.3 The Reward Process and Snell's Envelope; 6.4 Describing the Optimal Strategy; 6.5 The Likelihood-Ratio Test; 6.6 Applications; 6.7 Complement; Exercises; Historical Notes; 7. Optimal Sequential Control 7.1 An Example7.2 Preliminaries; 7.3 Controls; 7.4 Optimization; 7.5 Optimization Over Finite Controls; 7.6 Case Where the Index Set Is Finite; 7.7 Extension to General Index Sets; Exercises; Historical Notes; 8. Multiarmed Bandits; 8.1 Formulating the Problem; 8.2 Index Controls; 8.3 Gittins Indices; 8.4 Characterizing Optimal Controls; 8.5 Examples; Exercises; Historical Notes; 9. The Markovian Case; 9.1 Markov Chains and Superharmonic Functions; 9.2 Optimal Control of a Markov Chain; 9.3 The Special Case of a Random Walk 9.4 Control and Stopping at the Time of First Visit to a Set of States9.5 Markov Structures; Exercises; Historical Notes; 10. Optimal Switching Between Two Random Walks; 10.1 Formulating and Solving the Problem; 10.2 Some Properties of the Solution; 10.3 The Structure of the Solution; 10.4 Constructing the Switching Curves; 10.5 Characterizing the Type of the Solution; 10.6 Determining the Type of the Solution; Exercises; Historical Notes; Bibliography; Index of Notation; Index of Terms |
| Record Nr. | UNINA-9911020439303321 |
Cairoli R (Renzo), <1931-1994.>
|
||
| New York, : J. Wiley & Sons, c1996 | ||
| Lo trovi qui: Univ. Federico II | ||
| ||