Advanced simulation-based methods for optimal stopping and control : with applications in finance /
Saved in:
| Author / Creator: | Belomestny, Denis, author. |
|---|---|
| Imprint: | London, United Kingdom : Palgrave Macmillan, [2018] |
| Description: | 1 online resource |
| Language: | English |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11543304 |
Table of Contents:
- Intro; Acknowledgements; Contents; List of Figures; List of Tables; 1 Introduction; Part I Monte Carlo Techniques; 2 Elementary Monte Carlo Methods; 2.1 High-Dimensional Integration; 2.1.1 Numerical Evaluation on a Deterministic Grid; 2.1.2 Alternative: Monte Carlo Simulation; 2.1.3 Applications to Option Pricing; 2.2 Simulation of Random Variables; 2.2.1 Inverse Transform Method; 2.2.2 Box-MÃơller Method for Standard Normal r.v.; 2.2.3 Standard Normals by Marsaglia's Method; 2.2.4 Simulation of a General Density; 2.2.5 Variance Reduction.
- 2.3 Monte Carlo Construction of Stochastic Differential Equations (SDEs)2.3.1 Simulating European Options; 3 Variance Reduction for SDEs; 3.1 Introduction; 3.2 Control Variates for Strong Approximation Schemes; 3.2.1 Series Representation; 3.2.2 Integral Representation; 3.3 Regression Analysis; 3.3.1 Global Monte Carlo Regression Algorithm; 3.3.2 Piecewise Polynomial Regression; 3.3.3 Summary of the Algorithm; 3.4 Complexity Analysis; 3.4.1 Integral Approach; 3.4.2 Series Approach; 3.4.3 Discussion; 3.5 Numerical Results; 3.5.1 One-Dimensional Example; 3.5.2 Five-Dimensional Example.
- 4 Multilevel Methods4.1 Introduction; 4.2 Euler Scheme for Lévy-Driven SDEs; 4.3 Multilevel Path Simulation for Weak Euler Schemes; 4.3.1 Coupling Idea; 4.3.2 MLMC Algorithm; 4.4 Examples; 4.4.1 Diffusion Processes; 4.4.2 Jump Diffusion processes; 4.4.3 General Lévy Processes; 4.5 Numerical Experiments; 4.5.1 Diffusion Process; 4.5.2 Jump Diffusions; Part II Primal Methods for Optimal Stopping and Control; 5 General Problem Setups; 5.1 Optimal Stopping; 5.2 Generalization to Markovian Control Problems; 6 Primal Approximation Methods for Optimal Stopping; 6.1 Notation.
- 6.2 Methods Based on Dynamic Programming Principle6.3 Simulation-Based Optimization Algorithms; 6.4 Convergence Analysis; 6.5 Complexity Analysis; 7 Stochastic Policy Iteration Methods; 7.1 Policy Improvement, Iteration, and Stability; 7.2 Multilevel Simulation Based Policy Iteration; 7.2.1 Introduction; 7.2.2 Policy Iteration for Optimal Stopping; 7.2.3 Simulation Based Policy Iteration; 7.2.4 Standard Monte Carlo Approach; 7.2.5 Multilevel Monte Carlo Approach; 7.2.6 Numerical Comparison of the Two Estimators; 7.2.7 Numerical Example: American Max-Call; 7.2.8 Proofs.
- 7.2.9 Proof of Proposition 557.2.10 Proof of Theorem 58; 7.2.11 Proof of Theorem 59; 7.2.12 Appendix; 8 Regression Methods for Markovian Control Problems; 8.1 Setup Based on Reference Measure; 8.1.1 Algorithms Based on Local Estimators; 8.1.2 Global Regression Estimators; 8.2 Convergence Analysis of Regression Methods; 8.2.1 Convergence of Local Regression Estimators; 8.2.2 Convergence of Global Regression Estimators; 8.3 Dual Upper Bounds; 8.4 Numerical Example; 8.4.1 Some Results from the Theory of Empirical Processes; Part III Dual Methods for Optimal Stopping and Control.