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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

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內容詳細、豐富，從中獲益不小。

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書很新，速度很快，很滿意

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開捲有益處,不忘送書人

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金融數學

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活動時買的，還是挺劃算的，給個好評！

評分☆☆☆☆☆

金融數學

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很經典的一本教材，老師推薦的。

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這本書相當不錯，內容主要是關於數學金融方麵的。作者已有多部著作，頗受歡迎。專業性較強，需要相當的數學基礎。

評分☆☆☆☆☆

紀數學技術和計算機技術一樣成為任何一門科學發展過程中的必備工具。美國花旗銀行副總裁柯林斯（Collins）1995年3月6日在英國劍橋大學牛頓數學科學研究所的講演中敘述到：“在18世紀初，和牛頓同時代的著名數學傢伯努利曾宣稱：‘從事物理學研究而不懂數學的人實際上處理的是意義不大的東西。’那時候，這樣的說法對物理學而言是正確的，但對於銀行業而言不一定對。在18世紀，你可以沒有任何數學訓練而很好地運作銀行。過去對物理學而言是正確的說法現在對於銀行業也正確瞭。於是現在可以這樣說：‘從事銀行業工作而不懂數學的人實際上處理的是意義不大的東西’。”他還指齣：花旗銀行70%的業務依賴於數學，他還特彆強調，‘如果沒有數學發展起來的工具和技術，許多事情我們是一點辦法也沒有的……沒有數學我們不可能生存。”這裏銀行傢用他的經驗描述瞭數學的重要性。在冷戰結束後，美國原先在軍事係統工作的數以韆計的科學傢進入瞭華爾街，大規模的基金管理公司紛紛開始雇傭數學博士或物理學博士。這是一個重要信號：金融市場不是戰場，卻遠勝於戰場。但是市場和戰場都離不開復雜艱深，迅速的計算工作。

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