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[美] Fwu-Ranq Chang 著

齣版社： 世界圖書齣版公司

ISBN：9787510050442

版次：1

商品編碼：11181632

包裝：平裝

開本：24開

齣版時間：2013-01-01

頁數：326

內容簡介

　　"Stochastic optimization in continuous time"（AuthorFwu-Ranq Chang）is a rigorous but user-friendly book on the application of stochastic control theory to economics. A distinctive feature of the book is that math-ematical concepts are introduced in a language and terminology familiar to graduate students of economics.

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□]
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

前言/序言

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應用背景

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應用背景

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在現代的管理科學、工程技術、社會經濟、交通運輸、金融保險等諸多領域都存在著大量的最優化問題。與此同時，這些領域又毋庸置疑地存在著人為的模糊性或客觀的隨機性。然而一個復雜的決策問題通常處在這兩種不確定性因素混閤的環境之中，模糊隨機性就是一種具體的體現。那麼，模糊隨機環境下如何建立機會測度理論?如何建立單階段和多階段模糊隨機優化模型?又如何采用逼近方法求解這些優化模型?本書分彆迴答瞭這些問題。該書將介紹模糊隨機優化理論的最新研究成果，包括模糊隨機環境下的平均機會理論、靜態模糊隨機規劃、具有補償問題的兩階段模糊隨機規劃、優化模型的逼近方法及其收斂性等問題。本書可作為應用數學專業高年級大學生和運籌學與控製論專業研究生教材，也可作為從事運籌學、管理科學及信息科學研究的高校教師和科技人員的參考書。

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由於星地鏈路之間的主要傳輸介質是大氣，穿過路徑較長，大氣分子對於激光光束的吸收與散射將引起傳播方嚮上光能的衰減，因此傳輸信道中的大氣湍流是限製通信距離及通信係統性能的瓶頸之一，不僅需要考慮大氣對激光的吸收與散射，還必須考慮大氣的湍流效應。大氣湍流會使光載波在傳輸過程中隨機地改變其光束特性，緻使攜帶信息的光波的強度和相位在空間和時間上都呈現隨機起伏，造成閃爍現象，極大地降低瞭係統的成像質量或光束質量。基於隨機並行下降算法的自適應光學技術可以提高激光作用到目標上的聚集程度；降低空間目標在望遠鏡成像麵上的模糊程度，提高目標識彆的準確度，實現對目標的精跟蹤；提高激光通信係統的載波光束質量，降低係統的噪聲水平、提高數據傳輸速率等，在天文自適應成像領域已得到成功應用。

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第三：由於無需波前重構，大氣湍流帶來的閃爍不影響算法的迭代以及反饋裝置的數據采集，在大氣湍流較強或光束長程傳輸應用中有其獨特優勢[3]。