Applied stochastic control of jump diffusions /
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| Author / Creator: | Øksendal, B. K. (Bernt Karsten), 1945- author. |
|---|---|
| Edition: | Third edition. |
| Imprint: | Cham, Switzerland : Springer, 2019. |
| Description: | 1 online resource (xvi, 436 pages) : illustrations (some color) |
| Language: | English |
| Series: | Universitext, 0172-5939 Universitext, |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11873831 |
Table of Contents:
- Intro; Preface to the Third Edition; Preface to the Second Edition; Preface to the First Edition; Contents; 1 Stochastic Calculus with Lévy Processes; 1.1 Basic Definitions and Results on Lévy Processes; 1.2 The Itô Formula and Related Results; 1.3 Lévy Stochastic Differential Equations; 1.4 The Girsanov Theorem and Applications; 1.5 Exercises; 2 Financial Markets Modeled by Jump Diffusions; 2.1 Market Definitions and Arbitrage; 2.2 Hedging and Completeness; 2.3 Option Pricing; 2.3.1 European Options; 2.3.2 American Options; 2.4 Exercises; 3 Optimal Stopping of Jump Diffusions
- 3.1 A General Formulation and a Verification Theorem3.2 Applications and Examples; 3.3 Optimal Stopping with Delayed Information; 3.4 Exercises; 4 Backward Stochastic Differential Equations and Risk Measures; 4.1 Examples; 4.2 General BSDEs with Jumps; 4.3 Linear BSDEs; 4.4 Comparison Theorems; 4.5 Convex Risk Measures and BSDEs; 4.5.1 Dynamic Risk Measures; 4.5.2 A Dual Representation of Convex Risk Measures; 4.6 Exercises; 5 Stochastic Control of Jump Diffusions; 5.1 The Dynamic Programming Approach; 5.2 Stochastic Maximum Principles for Partial Information Control
- 5.2.1 A Sufficient Maximum Principle5.2.2 A Necessary Maximum Principle; 5.2.3 The Relation Between the Maximum Principle and Dynamic Programming; 5.2.4 Utility Maximization; 5.2.5 Mean-Variance Portfolio Selection; 5.3 The Maximum Principle with Infinite Horizon; 5.3.1 A Sufficient Maximum Principle; 5.3.2 A Necessary Maximum Principle; 5.4 Optimal Control of FBSDEs by Means of Stochastic HJB Equations; 5.4.1 Optimal Control of FBSDEs; 5.4.2 Applications in Mathematical Finance; 5.5 Optimal Control of Stochastic Delay Equations; 5.5.1 A Sufficient Maximum Principle
- 5.5.2 A Necessary Maximum Principle5.5.3 Time-Advanced BSDEs with Jumps; 5.5.4 Example: Optimal Consumption from a Cash Flow with Delay; 5.6 Exercises; 6 Stochastic Differential Games; 6.1 Stochastic Differential (Markov) Games, HJB-Isaacs Equations; 6.1.1 Entropic Risk Minimization Example; 6.2 Stochastic Maximum Principles; 6.2.1 General (Non-zero) Stochastic Differential Games; 6.2.2 The Zero-Sum Game Case; 6.2.3 Proofs of the Stochastic Maximum Principles; 6.2.4 Risk Minimization by FBSDE Games; 6.3 Mean-Field Games; 6.3.1 Two Motivating Examples
- 6.3.2 General Mean-Field Non-zero Sum Games6.3.3 A Sufficient Maximum Principle; 6.3.4 A Necessary Maximum Principle; 6.3.5 Application to Model Uncertainty Control; 6.3.6 The Zero-Sum Game Case; 6.3.7 The Single Player Case; 6.4 Exercises; 7 Combined Optimal Stopping and Stochastic Control of Jump Diffusions; 7.1 Introduction; 7.2 A General Mathematical Formulation; 7.3 Applications; 7.4 Exercises; 8 Singular Control for Jump Diffusions; 8.1 An Illustrating Example; 8.2 A General Formulation; 8.3 Application to Portfolio Optimization with Transaction Costs; 8.4 Exercises