金融數(shù)學(xué)方法

內(nèi)容概要

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.

書籍目錄

Preface1 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 Notes2 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 Notes3 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 Notes4 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 Notes5 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 Notes6 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 NotesAppendix A. Essential Supremum of a Family of Random VariablesAppendix B. On the Model of Section 1.1Appendix C. On Theorem 6.4.1Appendix D. Optimal Stopping for Continuons-Parameter ProcessesAppendix E. The Clark FormulaReferencesSymbol IndexIndex

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