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Advances in modeling and simulation : festschrift for Pierre L'Ecuyer / / Zdravko Botev [and three others], editors
| Advances in modeling and simulation : festschrift for Pierre L'Ecuyer / / Zdravko Botev [and three others], editors |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (426 pages) |
| Disciplina | 511.8 |
| Soggetto topico |
Mathematical models
Simulation methods Models matemàtics Mètodes de simulació |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-031-10193-6 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Acknowledgements -- Biography -- Contents -- Monte Carlo Methods for Pricing American Options -- 1 Introduction -- 2 American Option Pricing -- 3 Binomial Tree Method -- 4 Dynamic Programming Approach -- 4.1 Regression Methods -- 4.2 Malliavin Calculus -- 5 Control Variates -- 6 Numerical Experiments -- 7 Conclusion -- References -- Remarks on Lévy Process Simulation -- 1 Introduction -- 2 Lévy Processes -- 3 Main Examples -- 4 The ε-Algorithm -- 5 Using Complete Monotonicity Structure -- 6 Numerical Examples -- 7 Exact Simulation of X(h) and other Methods -- 8 Maxima, Minima and Other Path Functionals -- References -- Exact Sampling for the Maximum of Infinite Memory Gaussian Processes -- 1 Introduction -- 2 Basic Strategy -- 2.1 Milestone Events -- 2.2 Main Algorithm -- 3 Intermediate Steps in Algorithm 2 -- 4 Analysis of Algorithm 2 -- 4.1 Output Analysis -- 4.2 Complexity Analysis -- 5 Numerical Experiments -- 6 Conclusion -- References -- Truncated Multivariate Student Computations via Exponential Tilting -- 1 Introduction -- 2 Review of the Sequentially Tilted Proposal Density -- 3 Asymptotic Efficiency of the IS Estimator -- 4 Application to Constrained Linear Regression -- 5 Tobit Model Application -- 6 Application to ``Bayesian'' Splines for Non-negative Functions -- 7 The Reject-Regenerate Sampler -- 7.1 Nummelin Splitting of Transition Kernel -- 7.2 Rare-Event Robustness -- 8 Concluding Remarks -- References -- Quasi-Monte Carlo Methods in Portfolio Selection with Many Constraints -- 1 Introduction -- 2 Classical Portfolio Selection in a Nutshell -- 3 Portfolio Optimization with Many Constraints -- 4 Approximation of the Opportunity Set by Naïve Monte Carlo, and by Exponential Monte Carlo -- 5 Approximation of the Opportunity Set with Exponential QMC.
6 Approximating the Market Portfolio with MC, Exponential MC, and Exponential QMC -- 7 Approximating the Whole OS with MC, Exponential MC, and Exponential QMC -- 8 How to Calculate the Dispersion of a Sample Set in an OS? -- 9 Some Simulation Results -- 10 Conclusions, Outlook, and Further Practical Problem -- References -- Geometric-Moment Contraction of G/G/1 Waiting Times -- 1 Introduction -- 2 Main Results -- 3 Monte Carlo Results -- 3.1 M/M/1 Queue -- 3.2 M/G/1 Queues -- 4 Conclusions -- References -- Tractability of Approximation in the Weighted Korobov Space in the Worst-Case Setting -- 1 Introduction -- 2 Basic Definitions -- 2.1 Function Space Setting -- 2.2 Approximation in script upper H Subscript d comma alpha comma bold italic gammamathcalHd,α,γ -- 2.3 The Worst-Case Setting -- 2.4 Useful Relations -- 2.5 Relations to the Average-Case Setting -- 2.6 Notions of Tractability -- 3 The Results for normal upper A normal upper P normal upper P Subscript 2APP2 -- 4 The Results for normal upper A normal upper P normal upper P Subscript normal infinityAPPinfty -- 5 Overview and Formulation of Open Problems -- 5.1 Open Problems -- References -- Rare-Event Simulation via Neural Networks -- 1 Introduction -- 1.1 Background -- 2 Rare-Event Deep Learning -- 2.1 Networks and Loss Functions -- 2.2 Kernel Density Estimation -- 2.3 Training Procedure -- 2.4 Rare-Event Distribution -- 3 Experimental Results -- 3.1 Learning Normal Distributions -- 3.2 Normal Distribution Rare-Events -- 3.3 Learning Sum of Exponential Distributions -- 4 Conclusions and Further Research -- References -- Preintegration is Not Smoothing When Monotonicity Fails -- 1 Introduction -- 1.1 Related Work -- 1.2 The Problem -- 1.3 Informative Examples -- 1.4 Outline of This Paper -- 2 Smoothness Theorems in dd Dimensions -- 3 A High-Dimensional Example -- 4 Conclusion -- References. Combined Derivative Estimators -- 1 Introduction -- 2 Derivative Estimation -- 2.1 Background -- 2.2 Combined Estimators -- 2.3 Second Derivatives -- 2.4 Finite Difference Estimators and IPA -- 2.5 IPA and Randomized Score Functions -- 2.6 LRM Singularities -- 2.7 Generalized Likelihood Ratio Method -- 3 A Barrier Option Example -- 3.1 The Option Pricing Setting -- 3.2 The Barrier Option -- 3.3 A Combined IPA-LRM Estimator of Wang et al. ch10wang -- 3.4 GLR as a Combined IPA-LRM Estimator -- 4 Approaching Continuous Time: Averaging Low-Rank GLR Estimators -- 4.1 Approximating Continuous-Time Sensitivities -- 4.2 Averaging GLR Estimators -- 5 Concluding Remarks -- References -- A Central Limit Theorem For Empirical Quantiles in the Markov Chain Setting -- 1 Introduction -- 2 A Quantile Central Limit Theorem -- 3 A Uniform CLT for 1-Dependent Sequences -- 4 A Quantile Central Limit Theorem for Harris Processes -- 5 The Validity of Non-overlapping Batch-Means Estimation -- 6 Sufficient Conditions -- References -- Simulation of Markov Chains with Continuous State Space by Using Simple Stratified and Sudoku Latin Square Sampling -- 1 Introduction -- 2 Markov Chain Simulation with Stratified Sampling -- 2.1 Classical Monte Carlo -- 2.2 Simple Stratified Sampling -- 2.3 Sudoku Latin Square Sampling -- 3 Variance Bounds -- 3.1 Classical Monte Carlo -- 3.2 Simple Stratified Sampling -- 3.3 Sudoku Latin Square Sampling -- 4 Numerical Experiments -- 4.1 An Autoregressive Process -- 4.2 A European Put Option -- 4.3 Diffusion -- 5 Conclusions -- References -- Quasi-Random Sampling with Black Box or Acceptance-Rejection Inputs -- 1 Introduction -- 2 Methods for the Black Box Setting -- 2.1 Methods Based on the Empirical Quantile Function -- 2.2 Methods Based on a Generalized Pareto Approximation in the Tail -- 3 Combining AR with RQMC. 4 Application: Basket Option Pricing -- 5 Conclusion -- References -- A Generalized Transformed Density Rejection Algorithm -- 1 Introduction -- 2 Transformed Density Rejection with Inflection Points -- 3 Determine Signs of Second Derivatives -- 3.1 Initial Intervals -- 3.2 Splitting Intervals -- 4 The Algorithm -- 5 Applications -- 5.1 Generalized Hyperbolic Distribution -- 5.2 Truncated Distributions -- 5.3 Watson Distributions -- 6 Conclusions -- References -- Fast Automatic Bayesian Cubature Using Sobol' Sampling -- 1 Introduction -- 2 Bayesian Cubature -- 3 Digital Nets and Walsh Kernels -- 3.1 Digital Sequences -- 3.2 Covariance Kernels Constructed Via Walsh Functions -- 3.3 Eigenvector-Eigenvalue Decomposition of the Gram Matrix -- 4 Numerical Experiments -- 4.1 Multivariate Gaussian Probability -- 4.2 Keister's Example -- 4.3 Asian Option Pricing -- 4.4 Discussion -- 5 Conclusion and Future Work -- References -- Rendering Along the Hilbert Curve -- 1 Introduction -- 2 Visual Error in Image Synthesis -- 3 Enumerating Pixels Along the Hilbert Curve -- 3.1 Correlation in Space-Filling Curves -- 3.2 Blue-Noise Dithered Sampling -- 4 Progressive Image Synthesis -- 4.1 Deterministic Cranley-Patterson Rotation -- 4.2 Randomization -- 4.3 Contiguous Segments of one Low Discrepancy Sequence -- 4.4 Partitioning one Low Discrepancy Sequence -- 5 Results and Discussion -- 6 Conclusion -- References -- Array-RQMC to Speed up the Simulation for Estimating the Hitting-Time Distribution to a Rare Set of a Regenerative System -- 1 Introduction -- 2 Regenerative-Simulation-Based Estimators of the Distribution of the Hitting Time to a Rarely Visited Set -- 2.1 Assumptions and Notations -- 2.2 Exponential Limit -- 2.3 Exponential Estimators with Monte Carlo (MC) -- 2.4 Convolution Estimators with Monte Carlo. 3 Array-RQMC Implementation of Regenerative-Simulation-Based Estimators of Quantiles -- 3.1 RQMC and Array-RQMC -- 3.2 Array-RQMC Exponential and Convolution Estimators -- 4 Numerical Illustration of the Gain on the Simulation of an M/M/1 Queue -- 5 Conclusions -- References -- Foundations of Ranking & -- Selection for Simulation Optimization -- 1 Introduction -- 2 Set Up -- 3 The Normal Means Case -- 3.1 The Indifference-Zone (IZ) Formulation -- 3.2 R& -- S Based on ``Statistical Learning'' -- 3.3 A Convergence-Rate Perspective -- 3.4 Doing Better Than ``Rate Optimal'' -- 3.5 Common Random Numbers -- 3.6 ``Good Selection'' -- 3.7 Unknown Variances -- 3.8 A Note on Asymptotic Analysis -- 4 Parallel R& -- S -- 4.1 New Measures of Efficiency -- 4.2 New Objectives -- 4.3 Parting Thoughts -- 5 Other Formulations -- 6 Multi-armed Bandits -- References -- Where are the Logs? -- 1 Introduction -- 2 Background -- 3 Proof of the Lower Bound -- 4 Discrepancy and the Case of d equals 1d=1 -- 5 Empirical Investigations for d equals 2d=2 -- 6 Very Large mm for Sobol' Nets -- 7 Discussion -- References -- Network Reliability, Performability Metrics, Rare Events and Standard Monte Carlo -- 1 Introduction -- 2 Performability Metrics and Resilience -- 2.1 The Resilience Metric -- 2.2 Some Properties of Resilience -- 3 Using Standard Monte Carlo for Resilience-Based Analysis -- 3.1 The Standard Estimator -- 3.2 The Standard Estimator Efficiently Implemented in the Rare Event Case -- 3.3 Estimating the Resilience -- 3.4 Improving Algorithm B -- 3.5 Sensitivity Analysis -- 4 Examples and Discussions -- 5 Conclusions -- References. |
| Record Nr. | UNINA-9910633937903321 |
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Advances in modeling and simulation : festschrift for Pierre L'Ecuyer / / Zdravko Botev [and three others], editors
| Advances in modeling and simulation : festschrift for Pierre L'Ecuyer / / Zdravko Botev [and three others], editors |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (426 pages) |
| Disciplina | 511.8 |
| Soggetto topico |
Mathematical models
Simulation methods Models matemàtics Mètodes de simulació |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-031-10193-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Acknowledgements -- Biography -- Contents -- Monte Carlo Methods for Pricing American Options -- 1 Introduction -- 2 American Option Pricing -- 3 Binomial Tree Method -- 4 Dynamic Programming Approach -- 4.1 Regression Methods -- 4.2 Malliavin Calculus -- 5 Control Variates -- 6 Numerical Experiments -- 7 Conclusion -- References -- Remarks on Lévy Process Simulation -- 1 Introduction -- 2 Lévy Processes -- 3 Main Examples -- 4 The ε-Algorithm -- 5 Using Complete Monotonicity Structure -- 6 Numerical Examples -- 7 Exact Simulation of X(h) and other Methods -- 8 Maxima, Minima and Other Path Functionals -- References -- Exact Sampling for the Maximum of Infinite Memory Gaussian Processes -- 1 Introduction -- 2 Basic Strategy -- 2.1 Milestone Events -- 2.2 Main Algorithm -- 3 Intermediate Steps in Algorithm 2 -- 4 Analysis of Algorithm 2 -- 4.1 Output Analysis -- 4.2 Complexity Analysis -- 5 Numerical Experiments -- 6 Conclusion -- References -- Truncated Multivariate Student Computations via Exponential Tilting -- 1 Introduction -- 2 Review of the Sequentially Tilted Proposal Density -- 3 Asymptotic Efficiency of the IS Estimator -- 4 Application to Constrained Linear Regression -- 5 Tobit Model Application -- 6 Application to ``Bayesian'' Splines for Non-negative Functions -- 7 The Reject-Regenerate Sampler -- 7.1 Nummelin Splitting of Transition Kernel -- 7.2 Rare-Event Robustness -- 8 Concluding Remarks -- References -- Quasi-Monte Carlo Methods in Portfolio Selection with Many Constraints -- 1 Introduction -- 2 Classical Portfolio Selection in a Nutshell -- 3 Portfolio Optimization with Many Constraints -- 4 Approximation of the Opportunity Set by Naïve Monte Carlo, and by Exponential Monte Carlo -- 5 Approximation of the Opportunity Set with Exponential QMC.
6 Approximating the Market Portfolio with MC, Exponential MC, and Exponential QMC -- 7 Approximating the Whole OS with MC, Exponential MC, and Exponential QMC -- 8 How to Calculate the Dispersion of a Sample Set in an OS? -- 9 Some Simulation Results -- 10 Conclusions, Outlook, and Further Practical Problem -- References -- Geometric-Moment Contraction of G/G/1 Waiting Times -- 1 Introduction -- 2 Main Results -- 3 Monte Carlo Results -- 3.1 M/M/1 Queue -- 3.2 M/G/1 Queues -- 4 Conclusions -- References -- Tractability of Approximation in the Weighted Korobov Space in the Worst-Case Setting -- 1 Introduction -- 2 Basic Definitions -- 2.1 Function Space Setting -- 2.2 Approximation in script upper H Subscript d comma alpha comma bold italic gammamathcalHd,α,γ -- 2.3 The Worst-Case Setting -- 2.4 Useful Relations -- 2.5 Relations to the Average-Case Setting -- 2.6 Notions of Tractability -- 3 The Results for normal upper A normal upper P normal upper P Subscript 2APP2 -- 4 The Results for normal upper A normal upper P normal upper P Subscript normal infinityAPPinfty -- 5 Overview and Formulation of Open Problems -- 5.1 Open Problems -- References -- Rare-Event Simulation via Neural Networks -- 1 Introduction -- 1.1 Background -- 2 Rare-Event Deep Learning -- 2.1 Networks and Loss Functions -- 2.2 Kernel Density Estimation -- 2.3 Training Procedure -- 2.4 Rare-Event Distribution -- 3 Experimental Results -- 3.1 Learning Normal Distributions -- 3.2 Normal Distribution Rare-Events -- 3.3 Learning Sum of Exponential Distributions -- 4 Conclusions and Further Research -- References -- Preintegration is Not Smoothing When Monotonicity Fails -- 1 Introduction -- 1.1 Related Work -- 1.2 The Problem -- 1.3 Informative Examples -- 1.4 Outline of This Paper -- 2 Smoothness Theorems in dd Dimensions -- 3 A High-Dimensional Example -- 4 Conclusion -- References. Combined Derivative Estimators -- 1 Introduction -- 2 Derivative Estimation -- 2.1 Background -- 2.2 Combined Estimators -- 2.3 Second Derivatives -- 2.4 Finite Difference Estimators and IPA -- 2.5 IPA and Randomized Score Functions -- 2.6 LRM Singularities -- 2.7 Generalized Likelihood Ratio Method -- 3 A Barrier Option Example -- 3.1 The Option Pricing Setting -- 3.2 The Barrier Option -- 3.3 A Combined IPA-LRM Estimator of Wang et al. ch10wang -- 3.4 GLR as a Combined IPA-LRM Estimator -- 4 Approaching Continuous Time: Averaging Low-Rank GLR Estimators -- 4.1 Approximating Continuous-Time Sensitivities -- 4.2 Averaging GLR Estimators -- 5 Concluding Remarks -- References -- A Central Limit Theorem For Empirical Quantiles in the Markov Chain Setting -- 1 Introduction -- 2 A Quantile Central Limit Theorem -- 3 A Uniform CLT for 1-Dependent Sequences -- 4 A Quantile Central Limit Theorem for Harris Processes -- 5 The Validity of Non-overlapping Batch-Means Estimation -- 6 Sufficient Conditions -- References -- Simulation of Markov Chains with Continuous State Space by Using Simple Stratified and Sudoku Latin Square Sampling -- 1 Introduction -- 2 Markov Chain Simulation with Stratified Sampling -- 2.1 Classical Monte Carlo -- 2.2 Simple Stratified Sampling -- 2.3 Sudoku Latin Square Sampling -- 3 Variance Bounds -- 3.1 Classical Monte Carlo -- 3.2 Simple Stratified Sampling -- 3.3 Sudoku Latin Square Sampling -- 4 Numerical Experiments -- 4.1 An Autoregressive Process -- 4.2 A European Put Option -- 4.3 Diffusion -- 5 Conclusions -- References -- Quasi-Random Sampling with Black Box or Acceptance-Rejection Inputs -- 1 Introduction -- 2 Methods for the Black Box Setting -- 2.1 Methods Based on the Empirical Quantile Function -- 2.2 Methods Based on a Generalized Pareto Approximation in the Tail -- 3 Combining AR with RQMC. 4 Application: Basket Option Pricing -- 5 Conclusion -- References -- A Generalized Transformed Density Rejection Algorithm -- 1 Introduction -- 2 Transformed Density Rejection with Inflection Points -- 3 Determine Signs of Second Derivatives -- 3.1 Initial Intervals -- 3.2 Splitting Intervals -- 4 The Algorithm -- 5 Applications -- 5.1 Generalized Hyperbolic Distribution -- 5.2 Truncated Distributions -- 5.3 Watson Distributions -- 6 Conclusions -- References -- Fast Automatic Bayesian Cubature Using Sobol' Sampling -- 1 Introduction -- 2 Bayesian Cubature -- 3 Digital Nets and Walsh Kernels -- 3.1 Digital Sequences -- 3.2 Covariance Kernels Constructed Via Walsh Functions -- 3.3 Eigenvector-Eigenvalue Decomposition of the Gram Matrix -- 4 Numerical Experiments -- 4.1 Multivariate Gaussian Probability -- 4.2 Keister's Example -- 4.3 Asian Option Pricing -- 4.4 Discussion -- 5 Conclusion and Future Work -- References -- Rendering Along the Hilbert Curve -- 1 Introduction -- 2 Visual Error in Image Synthesis -- 3 Enumerating Pixels Along the Hilbert Curve -- 3.1 Correlation in Space-Filling Curves -- 3.2 Blue-Noise Dithered Sampling -- 4 Progressive Image Synthesis -- 4.1 Deterministic Cranley-Patterson Rotation -- 4.2 Randomization -- 4.3 Contiguous Segments of one Low Discrepancy Sequence -- 4.4 Partitioning one Low Discrepancy Sequence -- 5 Results and Discussion -- 6 Conclusion -- References -- Array-RQMC to Speed up the Simulation for Estimating the Hitting-Time Distribution to a Rare Set of a Regenerative System -- 1 Introduction -- 2 Regenerative-Simulation-Based Estimators of the Distribution of the Hitting Time to a Rarely Visited Set -- 2.1 Assumptions and Notations -- 2.2 Exponential Limit -- 2.3 Exponential Estimators with Monte Carlo (MC) -- 2.4 Convolution Estimators with Monte Carlo. 3 Array-RQMC Implementation of Regenerative-Simulation-Based Estimators of Quantiles -- 3.1 RQMC and Array-RQMC -- 3.2 Array-RQMC Exponential and Convolution Estimators -- 4 Numerical Illustration of the Gain on the Simulation of an M/M/1 Queue -- 5 Conclusions -- References -- Foundations of Ranking & -- Selection for Simulation Optimization -- 1 Introduction -- 2 Set Up -- 3 The Normal Means Case -- 3.1 The Indifference-Zone (IZ) Formulation -- 3.2 R& -- S Based on ``Statistical Learning'' -- 3.3 A Convergence-Rate Perspective -- 3.4 Doing Better Than ``Rate Optimal'' -- 3.5 Common Random Numbers -- 3.6 ``Good Selection'' -- 3.7 Unknown Variances -- 3.8 A Note on Asymptotic Analysis -- 4 Parallel R& -- S -- 4.1 New Measures of Efficiency -- 4.2 New Objectives -- 4.3 Parting Thoughts -- 5 Other Formulations -- 6 Multi-armed Bandits -- References -- Where are the Logs? -- 1 Introduction -- 2 Background -- 3 Proof of the Lower Bound -- 4 Discrepancy and the Case of d equals 1d=1 -- 5 Empirical Investigations for d equals 2d=2 -- 6 Very Large mm for Sobol' Nets -- 7 Discussion -- References -- Network Reliability, Performability Metrics, Rare Events and Standard Monte Carlo -- 1 Introduction -- 2 Performability Metrics and Resilience -- 2.1 The Resilience Metric -- 2.2 Some Properties of Resilience -- 3 Using Standard Monte Carlo for Resilience-Based Analysis -- 3.1 The Standard Estimator -- 3.2 The Standard Estimator Efficiently Implemented in the Rare Event Case -- 3.3 Estimating the Resilience -- 3.4 Improving Algorithm B -- 3.5 Sensitivity Analysis -- 4 Examples and Discussions -- 5 Conclusions -- References. |
| Record Nr. | UNISA-996499866203316 |
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Handbook of Monte Carlo methods / / Dirk P. Kroese, Thomas Taimre, Zdravko I. Botev
| Handbook of Monte Carlo methods / / Dirk P. Kroese, Thomas Taimre, Zdravko I. Botev |
| Autore | Kroese Dirk P |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley, 2011 |
| Descrizione fisica | 1 online resource (752 p.) |
| Disciplina | 518/.282 |
| Altri autori (Persone) |
TaimreThomas <1983->
BotevZdravko I. <1982-> |
| Collana | Wiley series in probability and statistics |
| Soggetto topico | Monte Carlo method |
| ISBN |
1-283-07242-4
9786613072429 1-118-01495-2 1-118-01496-0 1-118-01494-4 |
| Classificazione | MAT029000 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910141148203321 |
Kroese Dirk P
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| Hoboken, N.J., : Wiley, 2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||