《連續時間中的隨機最佳化》對數學方法的討論更加直觀，並且用大量的經濟例子來說明，更重要的是數學概念的引入在語言和術語上是經濟專業的研究生所熟悉的。儘管許多論題在數學、經濟和金融書中都是比較普遍的，但仍然用大量的經濟學實例加以解釋。書中強調了隨機微積分的重點和非重點，需要提醒讀者的是許多經濟學家所想要的特定結果和觀點並沒有擴展至隨機模型中。隨機控制問題是確定最佳化策略函式必須的，第五章致力於用各種途徑尋找隨它的值函式的封閉形式表示。書中有大量的練習，每章末包含註解和建議閱讀文獻。
基本介紹
- 書名：連續時間中的隨機最佳化
- 作者：Fwu-Ranq Chang
- 出版社：世界圖書出版公司北京公司
- 頁數：326頁
- 開本：24
- 品牌：世界圖書出版公司北京公司
- 外文名：Stochastic Optimization in Continuous Time
- 類型：科學與自然
- 出版日期：2013年1月1日
- 語種：簡體中文, 英語
- ISBN：9787510050442
基本介紹,內容簡介,作者簡介,圖書目錄,編輯推薦,目錄,
基本介紹
內容簡介
《連續時間中的隨機最佳化》由世界圖書出版公司北京公司出版。
作者簡介
作者：（美國）Fwu-Ranq Chang
圖書目錄
List of Figures
Preface
1 Probability Theory
1.1 Introduction
1.2 Stochastic Processes
1.2.1 In formation Sets and a-Algebras
1.2.2 The Cantor Set
1.2.3 Borel-Cantelli Lemmas
1.2.4 Distribution Functions and Stochastic Processes
1.3 Conditional Expectation
1.3.1 Conditional Probability
1.3.2 Conditional Expectation
1.3.3 Change of Variables
1.4 Notes and Further Readings
2 Wiener Processes
2.1 introduction
2.2 A Heuristic Approach
2.2.1 From Random Walks to Wiener Process
2.2.2 Some Basic Properties of the Wiener Process
2.3 Markov Processes
2.3.1 Introduction
2.3.2 Transition Probability
2.3.3 Diffusion Processes
2.4 Wiener Processes
2.4.1 How to Generate More Wiener Processes
2.4.2 Differentiability of Sample Functions
2.4.3 Stopping Times
2.4.4 The Zero Set
2.4.5 Bounded Variations and the Irregularity of the
Wiener Process
2.5 Notes and Further Readings
3 Stochastic Calculus
3.1 Introduction
3.2 A Heuristic Approach
3.2.1 ls □ (s X )dWs Riemarm Integrable?
3.2.2 The Choice of□ Matters
3.2.3 In Search of the Class of Functions for a (s, w)
3.3 The Ito Integral
3.3.1 Definition
3.3.2 Martingales
3.4 lto's Lemma: Autonomous Case
3.4.1 Ito's Lemma
3.4.2 Geometric Brownian Motion
3.4.3 Population Dynamics
3.4.4 Additive Shocks or Multiplicative Shocks
3.4.5 Multiple Sources of Uncertainty
3.4.6 Multivariate lto's Lemma
3.5 Ito's Lemma for Time-Dependent Functions
3.5.1 Euler's Homogeneous Differential Equation and the Heat Equation
3.5.2 Black-Scholes Formula
3.5.3 Irreversible Investment
3.5.4 Budget Equation for an Investor
3.5.5 Ito's Lemma: General Form
3.6 Notes and Further Readings
4 Stochastic Dynamic Programming
4.1 Introduction
4.2 Bellman Equation
4.2.1 Infinite-Horizon Problems
4.2.2 Verification Theorem
4.2.3 Finite-Horizon Problems
4.2.4 Existence and Differentiability of the Value Function
4.3 Economic Applications
4.3.1 Consumption and Portfolio Rules
4.3.2 Index Bonds
4.3.3 Exhaustible Resources
4.3.4 Adjustment Costs and (Reversible) Investment
4.3.5 Uncertain Lifetimes and Life Insurance
4.4 Extension: Reeursive Utility
4.4.1 Bellman Equation with Recursive Utility
4.4.2 Effects of Reeursivity: Deterministic Case
4.5 Notes and Further Readings
5 How to Solve it
5.1 Introduction
5.2 HARA Functions
5.2.1 The Meaning of Each Parameter
5.2.2 Closed-Form Representations
5.3 Trial and Error
5.3.1 Linear-Quadratic Models
5.3.2 Linear-HARA models
5.3.3 Linear-Concave Models
5.3,4 Nonlinear-Concave Models
5.4 Symmetry
5.4.1 Linear-Quadratic Model Revisited
5.4.2 Merton's Model Revisited
5.4.3 Fischer's Index Bond Model
5.4.4 Life Insurance
5.5 The Substitution Method
5.6 Martingale Representation Method
5.6.1 Girsanov Transformation
5.6.2 Example: A Portfolio Problem
5.6.3 Which 8 to Choose?
5.6.4 A Transformed Problem
5.7 Inverse Optimum Method
5.7.1 The Inverse Optimal Problem: Certainty Case
5.7.2 The Inverse Optimal Problem: Stochastic Case
5.7.3 Inverse Optimal Problem of Merton's Model
5.8 Notes and Further Readings
6 Boundaries and Absorbing Barriers
6.1 Introduction
6.2 Nonnegativity Constraint
6.2.1 Issues and Problems
6.2.2 Comparison Theorems
6.2.3 Chang and Malliaris's Reflection Method
6.2.4 Inaccessible Boundaries
6.3 Other Constraints
6.3.1 A Portfolio Problem with Borrowing CoosWaints
6.3.2 Viscosity Solutions
6.4 Stopping Rules-Certainty Case
6.4.1 The Baumol-Tobin Model
6.4.2 A Dynamic Model of Money Demand
6.4.3 The Tree-Cutting Problem
6.5 The Expected Discount Factor
6.5.1 Fundamental Equation for Ex(e-rt)
6.5.2 One Absorbing Barrier
6.5.3 Two Absorbing Barriers
6.6 Optimal Stopping Times
6.6.1 Dynamic and Stochastic Demand for Money
6.6.2 Stochastic Tree-Cutting and Rotation Problems
6.6.3 Investment Timing
6.7 Notes and Further Readings
A Miscellaneous Applications and Exercises
Bibliography
Index
Preface
1 Probability Theory
1.1 Introduction
1.2 Stochastic Processes
1.2.1 In formation Sets and a-Algebras
1.2.2 The Cantor Set
1.2.3 Borel-Cantelli Lemmas
1.2.4 Distribution Functions and Stochastic Processes
1.3 Conditional Expectation
1.3.1 Conditional Probability
1.3.2 Conditional Expectation
1.3.3 Change of Variables
1.4 Notes and Further Readings
2 Wiener Processes
2.1 introduction
2.2 A Heuristic Approach
2.2.1 From Random Walks to Wiener Process
2.2.2 Some Basic Properties of the Wiener Process
2.3 Markov Processes
2.3.1 Introduction
2.3.2 Transition Probability
2.3.3 Diffusion Processes
2.4 Wiener Processes
2.4.1 How to Generate More Wiener Processes
2.4.2 Differentiability of Sample Functions
2.4.3 Stopping Times
2.4.4 The Zero Set
2.4.5 Bounded Variations and the Irregularity of the
Wiener Process
2.5 Notes and Further Readings
3 Stochastic Calculus
3.1 Introduction
3.2 A Heuristic Approach
3.2.1 ls □ (s X )dWs Riemarm Integrable?
3.2.2 The Choice of□ Matters
3.2.3 In Search of the Class of Functions for a (s, w)
3.3 The Ito Integral
3.3.1 Definition
3.3.2 Martingales
3.4 lto's Lemma: Autonomous Case
3.4.1 Ito's Lemma
3.4.2 Geometric Brownian Motion
3.4.3 Population Dynamics
3.4.4 Additive Shocks or Multiplicative Shocks
3.4.5 Multiple Sources of Uncertainty
3.4.6 Multivariate lto's Lemma
3.5 Ito's Lemma for Time-Dependent Functions
3.5.1 Euler's Homogeneous Differential Equation and the Heat Equation
3.5.2 Black-Scholes Formula
3.5.3 Irreversible Investment
3.5.4 Budget Equation for an Investor
3.5.5 Ito's Lemma: General Form
3.6 Notes and Further Readings
4 Stochastic Dynamic Programming
4.1 Introduction
4.2 Bellman Equation
4.2.1 Infinite-Horizon Problems
4.2.2 Verification Theorem
4.2.3 Finite-Horizon Problems
4.2.4 Existence and Differentiability of the Value Function
4.3 Economic Applications
4.3.1 Consumption and Portfolio Rules
4.3.2 Index Bonds
4.3.3 Exhaustible Resources
4.3.4 Adjustment Costs and (Reversible) Investment
4.3.5 Uncertain Lifetimes and Life Insurance
4.4 Extension: Reeursive Utility
4.4.1 Bellman Equation with Recursive Utility
4.4.2 Effects of Reeursivity: Deterministic Case
4.5 Notes and Further Readings
5 How to Solve it
5.1 Introduction
5.2 HARA Functions
5.2.1 The Meaning of Each Parameter
5.2.2 Closed-Form Representations
5.3 Trial and Error
5.3.1 Linear-Quadratic Models
5.3.2 Linear-HARA models
5.3.3 Linear-Concave Models
5.3,4 Nonlinear-Concave Models
5.4 Symmetry
5.4.1 Linear-Quadratic Model Revisited
5.4.2 Merton's Model Revisited
5.4.3 Fischer's Index Bond Model
5.4.4 Life Insurance
5.5 The Substitution Method
5.6 Martingale Representation Method
5.6.1 Girsanov Transformation
5.6.2 Example: A Portfolio Problem
5.6.3 Which 8 to Choose?
5.6.4 A Transformed Problem
5.7 Inverse Optimum Method
5.7.1 The Inverse Optimal Problem: Certainty Case
5.7.2 The Inverse Optimal Problem: Stochastic Case
5.7.3 Inverse Optimal Problem of Merton's Model
5.8 Notes and Further Readings
6 Boundaries and Absorbing Barriers
6.1 Introduction
6.2 Nonnegativity Constraint
6.2.1 Issues and Problems
6.2.2 Comparison Theorems
6.2.3 Chang and Malliaris's Reflection Method
6.2.4 Inaccessible Boundaries
6.3 Other Constraints
6.3.1 A Portfolio Problem with Borrowing CoosWaints
6.3.2 Viscosity Solutions
6.4 Stopping Rules-Certainty Case
6.4.1 The Baumol-Tobin Model
6.4.2 A Dynamic Model of Money Demand
6.4.3 The Tree-Cutting Problem
6.5 The Expected Discount Factor
6.5.1 Fundamental Equation for Ex(e-rt)
6.5.2 One Absorbing Barrier
6.5.3 Two Absorbing Barriers
6.6 Optimal Stopping Times
6.6.1 Dynamic and Stochastic Demand for Money
6.6.2 Stochastic Tree-Cutting and Rotation Problems
6.6.3 Investment Timing
6.7 Notes and Further Readings
A Miscellaneous Applications and Exercises
Bibliography
Index
編輯推薦
《連續時間中的隨機最佳化》由世界圖書出版公司北京公司出版。
目錄
List of Figures
Preface
1 Probability Theory
1.1 Introduction
1.2 Stochastic Processes
1.2.1 In formation Sets and a-Algebras
1.2.2 The Cantor Set
1.2.3 Borel-Cantelli Lemmas
1.2.4 Distribution Functions and Stochastic Processes
1.3 Conditional Expectation
1.3.1 Conditional Probability
1.3.2 Conditional Expectation
1.3.3 Change of Variables
1.4 Notes and Further Readings
2 Wiener Processes
2.1 introduction
2.2 A Heuristic Approach
2.2.1 From Random Walks to Wiener Process
2.2.2 Some Basic Properties of the Wiener Process
2.3 Markov Processes
2.3.1 Introduction
2.3.2 Transition Probability
2.3.3 Diffusion Processes
2.4 Wiener Processes
2.4.1 How to Generate More Wiener Processes
2.4.2 Differentiability of Sample Functions
2.4.3 Stopping Times
2.4.4 The Zero Set
2.4.5 Bounded Variations and the Irregularity of the
Wiener Process
2.5 Notes and Further Readings
3 Stochastic Calculus
3.1 Introduction
3.2 A Heuristic Approach
3.2.1 ls □ (s X )dWs Riemarm Integrable?
3.2.2 The Choice of□ Matters
3.2.3 In Search of the Class of Functions for a (s, w)
3.3 The Ito Integral
3.3.1 Definition
3.3.2 Martingales
3.4 lto's Lemma: Autonomous Case
3.4.1 Ito's Lemma
3.4.2 Geometric Brownian Motion
3.4.3 Population Dynamics
3.4.4 Additive Shocks or Multiplicative Shocks
3.4.5 Multiple Sources of Uncertainty
3.4.6 Multivariate lto's Lemma
3.5 Ito's Lemma for Time-Dependent Functions
3.5.1 Euler's Homogeneous Differential Equation and the Heat Equation
3.5.2 Black-Scholes Formula
3.5.3 Irreversible Investment
3.5.4 Budget Equation for an Investor
3.5.5 Ito's Lemma: General Form
3.6 Notes and Further Readings
4 Stochastic Dynamic Programming
4.1 Introduction
4.2 Bellman Equation
4.2.1 Infinite-Horizon Problems
4.2.2 Verification Theorem
4.2.3 Finite-Horizon Problems
4.2.4 Existence and Differentiability of the Value Function
4.3 Economic Applications
4.3.1 Consumption and Portfolio Rules
4.3.2 Index Bonds
4.3.3 Exhaustible Resources
4.3.4 Adjustment Costs and (Reversible) Investment
4.3.5 Uncertain Lifetimes and Life Insurance
4.4 Extension: Reeursive Utility
4.4.1 Bellman Equation with Recursive Utility
4.4.2 Effects of Reeursivity: Deterministic Case
4.5 Notes and Further Readings
5 How to Solve it
5.1 Introduction
5.2 HARA Functions
5.2.1 The Meaning of Each Parameter
5.2.2 Closed-Form Representations
5.3 Trial and Error
5.3.1 Linear-Quadratic Models
5.3.2 Linear-HARA models
5.3.3 Linear-Concave Models
5.3,4 Nonlinear-Concave Models
5.4 Symmetry
5.4.1 Linear-Quadratic Model Revisited
5.4.2 Merton's Model Revisited
5.4.3 Fischer's Index Bond Model
5.4.4 Life Insurance
5.5 The Substitution Method
5.6 Martingale Representation Method
5.6.1 Girsanov Transformation
5.6.2 Example: A Portfolio Problem
5.6.3 Which 8 to Choose?
5.6.4 A Transformed Problem
5.7 Inverse Optimum Method
5.7.1 The Inverse Optimal Problem: Certainty Case
5.7.2 The Inverse Optimal Problem: Stochastic Case
5.7.3 Inverse Optimal Problem of Merton's Model
5.8 Notes and Further Readings
6 Boundaries and Absorbing Barriers
6.1 Introduction
6.2 Nonnegativity Constraint
6.2.1 Issues and Problems
6.2.2 Comparison Theorems
6.2.3 Chang and Malliaris's Reflection Method
6.2.4 Inaccessible Boundaries
6.3 Other Constraints
6.3.1 A Portfolio Problem with Borrowing CoosWaints
6.3.2 Viscosity Solutions
6.4 Stopping Rules-Certainty Case
6.4.1 The Baumol-Tobin Model
6.4.2 A Dynamic Model of Money Demand
6.4.3 The Tree-Cutting Problem
6.5 The Expected Discount Factor
6.5.1 Fundamental Equation for Ex(e-rt)
6.5.2 One Absorbing Barrier
6.5.3 Two Absorbing Barriers
6.6 Optimal Stopping Times
6.6.1 Dynamic and Stochastic Demand for Money
6.6.2 Stochastic Tree-Cutting and Rotation Problems
6.6.3 Investment Timing
6.7 Notes and Further Readings
A Miscellaneous Applications and Exercises
Bibliography
Index
Preface
1 Probability Theory
1.1 Introduction
1.2 Stochastic Processes
1.2.1 In formation Sets and a-Algebras
1.2.2 The Cantor Set
1.2.3 Borel-Cantelli Lemmas
1.2.4 Distribution Functions and Stochastic Processes
1.3 Conditional Expectation
1.3.1 Conditional Probability
1.3.2 Conditional Expectation
1.3.3 Change of Variables
1.4 Notes and Further Readings
2 Wiener Processes
2.1 introduction
2.2 A Heuristic Approach
2.2.1 From Random Walks to Wiener Process
2.2.2 Some Basic Properties of the Wiener Process
2.3 Markov Processes
2.3.1 Introduction
2.3.2 Transition Probability
2.3.3 Diffusion Processes
2.4 Wiener Processes
2.4.1 How to Generate More Wiener Processes
2.4.2 Differentiability of Sample Functions
2.4.3 Stopping Times
2.4.4 The Zero Set
2.4.5 Bounded Variations and the Irregularity of the
Wiener Process
2.5 Notes and Further Readings
3 Stochastic Calculus
3.1 Introduction
3.2 A Heuristic Approach
3.2.1 ls □ (s X )dWs Riemarm Integrable?
3.2.2 The Choice of□ Matters
3.2.3 In Search of the Class of Functions for a (s, w)
3.3 The Ito Integral
3.3.1 Definition
3.3.2 Martingales
3.4 lto's Lemma: Autonomous Case
3.4.1 Ito's Lemma
3.4.2 Geometric Brownian Motion
3.4.3 Population Dynamics
3.4.4 Additive Shocks or Multiplicative Shocks
3.4.5 Multiple Sources of Uncertainty
3.4.6 Multivariate lto's Lemma
3.5 Ito's Lemma for Time-Dependent Functions
3.5.1 Euler's Homogeneous Differential Equation and the Heat Equation
3.5.2 Black-Scholes Formula
3.5.3 Irreversible Investment
3.5.4 Budget Equation for an Investor
3.5.5 Ito's Lemma: General Form
3.6 Notes and Further Readings
4 Stochastic Dynamic Programming
4.1 Introduction
4.2 Bellman Equation
4.2.1 Infinite-Horizon Problems
4.2.2 Verification Theorem
4.2.3 Finite-Horizon Problems
4.2.4 Existence and Differentiability of the Value Function
4.3 Economic Applications
4.3.1 Consumption and Portfolio Rules
4.3.2 Index Bonds
4.3.3 Exhaustible Resources
4.3.4 Adjustment Costs and (Reversible) Investment
4.3.5 Uncertain Lifetimes and Life Insurance
4.4 Extension: Reeursive Utility
4.4.1 Bellman Equation with Recursive Utility
4.4.2 Effects of Reeursivity: Deterministic Case
4.5 Notes and Further Readings
5 How to Solve it
5.1 Introduction
5.2 HARA Functions
5.2.1 The Meaning of Each Parameter
5.2.2 Closed-Form Representations
5.3 Trial and Error
5.3.1 Linear-Quadratic Models
5.3.2 Linear-HARA models
5.3.3 Linear-Concave Models
5.3,4 Nonlinear-Concave Models
5.4 Symmetry
5.4.1 Linear-Quadratic Model Revisited
5.4.2 Merton's Model Revisited
5.4.3 Fischer's Index Bond Model
5.4.4 Life Insurance
5.5 The Substitution Method
5.6 Martingale Representation Method
5.6.1 Girsanov Transformation
5.6.2 Example: A Portfolio Problem
5.6.3 Which 8 to Choose?
5.6.4 A Transformed Problem
5.7 Inverse Optimum Method
5.7.1 The Inverse Optimal Problem: Certainty Case
5.7.2 The Inverse Optimal Problem: Stochastic Case
5.7.3 Inverse Optimal Problem of Merton's Model
5.8 Notes and Further Readings
6 Boundaries and Absorbing Barriers
6.1 Introduction
6.2 Nonnegativity Constraint
6.2.1 Issues and Problems
6.2.2 Comparison Theorems
6.2.3 Chang and Malliaris's Reflection Method
6.2.4 Inaccessible Boundaries
6.3 Other Constraints
6.3.1 A Portfolio Problem with Borrowing CoosWaints
6.3.2 Viscosity Solutions
6.4 Stopping Rules-Certainty Case
6.4.1 The Baumol-Tobin Model
6.4.2 A Dynamic Model of Money Demand
6.4.3 The Tree-Cutting Problem
6.5 The Expected Discount Factor
6.5.1 Fundamental Equation for Ex(e-rt)
6.5.2 One Absorbing Barrier
6.5.3 Two Absorbing Barriers
6.6 Optimal Stopping Times
6.6.1 Dynamic and Stochastic Demand for Money
6.6.2 Stochastic Tree-Cutting and Rotation Problems
6.6.3 Investment Timing
6.7 Notes and Further Readings
A Miscellaneous Applications and Exercises
Bibliography
Index
