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內容簡介

This book is intended for readers who are quite familiar with probability and stochastic processes but know little or nothing about finance. It is written in the definition/theorem/proof style of modern mathematics and attempts to explain as much of the finance motivation and terminology as possible.

目錄

Preface
1 A Brownian Model of Financial Markets
1.1 Stocks and a Money Market
1.2 Portfolio and Gains Processes
1.3 Income and Wealth Processes
1.4 Arbitrage and Market Viability
1.5 Standard Financial Markets
1.6 Completeness of Financial Markets
1.7 Financial Markets with an Infinite Planning Horizon
1.8 Notes

2 Contingent Claim Valuation in a Complete Market
2.1 Introduction
2.2 European Contingent Claims
2.3 Forward and Futures Contracts
2.4 European Options in a Constant-Coefficient Market
2.5 American Contingent Claims
2.6 The American Call Option
2.7 The American Put Option
2.8 Notes
3 Single-Agent Consumption and Investment
3.1 Introduction
3.2 The Financial Market
3.3 Consumption and Portfolio Processes
3.4 Utility Functions
3.5 The Optimization Problems
3.6 Utility from Consumption and Terminal Wealth
3.7 Utility from Consumption or Terminal Wealth
3.8 Deterministic Coefficients
3.9 Consumption and Investment on an Infinite Horizon
3.10 Maximization of the Growth Rate of Wealth
3.11 Notes

4 Equilibrium in a Complete Market
4.1 Introduction
4.2 Agents, Endowments, and Utility Functions
4.3 The Financial Market: Consumption and Portfolio Processes
4.4 The Individual Optimization Problems
4.5 Equilibrium and the Representative Agent
4.6 Existence and Uniqueness of Equilibrium
4.7 Examples
4.8 Notes

5 Contingent Claims in Incomplete Markets
5.1 Introduction
5.2 The Model
5.3 Upper Hedging Price
5.4 Convex Sets and Support Functions
5.5 A Family of Auxiliary Markets
5.6 The Main Hedging Result
5.7 Upper Hedging with Constant Coefficients
5.8 Optimal Dual Processes
5.9 Lower Hedging Price
5.10 Lower Hedging with Constant Coefficients
5.11 Notes

6 Constrained Consumption and Investment
6.1 Introduction
6.2 Utility Maximization with Constraints
6.3 A Family of Unconstrained Problems
6.4 Equivalent Optimality Conditions
6.5 Duality and Existence
6.6 Deterministic Coefficients, Cone Constraints
6.7 Incomplete Markets
6.8 Higher Interest Rate for Borrowing Than for Investing
6.9 Notes
Appendix A. Essential Supremum of a Family of Random Variables
Appendix B. On the Model of Section 1.1
Appendix C. On Theorem 6.4.1
Appendix D. Optimal Stopping for Continuons-Parameter Processes
Appendix E. The Clark Formula
References
Symbol Index
Index

前言/序言

金融數學方法 下載 mobi epub pdf txt 電子書 格式

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21世

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能迴避這樣一個事實：受過高等教育的專業人士都可以讀懂國內經濟類，金融類核心期刊，但國內金融學專業的本科生卻很難讀懂本專業的國際核心期刊《Journal of Finance》，證券投資基金經理少有人去閱讀《Joural of Portfolio Management》，其原因不在於外語的熟練程度，而在於內容和研究方法上的差異，國內較多停留在以描述性分析為主著重描述金融的定義，市場的劃分及金融組織等，或稱為描述金融；而國外學術界以及實務界則以數量性分析為主，比如資本資産定價原理，衍生資産的復製方法等，或稱為分析金融，即使在國內金融學的教材中，雖然涉及到瞭標的資産（Underlying asset）和衍生資産（Derivative asset）定價，但對公式提齣的原文證明也予以迴避，這種現象是不閤理的，産生這種現象的原因有如下幾個方麵：首先，根據研究方法的不同，我國金融學科既可以歸到我國哲學社會科學規劃辦公室，也可以歸到國傢自然科學基金委員會管理科學部，前者占主要地位，且這支隊伍大多來自經濟轉軌前的

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