Advances in Modeling and Simulation: Festschrift for Pierre L'Ecuyer

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