《shreve(金融随机分析习题解答)》.docxVIP

Stochastic Calculus Solution for Finance, Volume I and II of Exercise Problems Yan Zeng August 20,2007 1 Contents 1 Stochastic Calculus for Finance I: The Binomial Asset Pricing Model 3 1.1 The Binomial No-Arbitrage Pricing Model 3 1.2 Probability Theory on Coin Toss Space 6 1.3 State Prices 1.4 American Derivative Securities 13 1.5 Random Walk 16 1.6 Interest-Rate-Dependent Assets 9 2 Stochastic Calculus for Finance Ⅱ: Continuous-Time Models 23 2.1 General Probability Theory 3 2.2 Information and Conditioning 7 2.3 Brownian Motion 1 2.4 Stochastic Calculus 34 2.5 Risk.Neutral Pricing 2.6 Connections with Partial Diferentiai Equations 创力文档 2.7 Exotic Options axb118.cm 2.8 American Derivative Securities 高清无水 2.9 Change of Numeraire 1 2.10 Term-Structure Models 6 2.11 Introduction to Jump Processes 83 2 This is a solution manual for the two-volume textbook Stochastic calculus for finance, by Steven Shreve. If you have any comments or find any typos/errors, please email me at yz44@. The current version omits the following problems. Volume I: 1.5,3.3,3.4,5.7;Volume Ⅱ: 3.9,7. 1,7.2, 7.5-7.9,10.8,10.9,10.10. Acknowledgment I thank Hua Li (a graduate student at Brown University) for reading through this solution mannal and communicating to me several mistakes/typos. I also thank Hideki Murakami for pointing out a typo in Exercise 4.3,Volume Ⅱ. 3 Chapter 1 Stochastic Calculus for Finance I: The Binomial Asset Pricing Model 1.1 The Binomial No-Arbitrage Pricing Model 1.1. Proof. If we get the up sate,then X?=X?(H)= △quS?+(1+r)(Xo-A?So);if we get the down state, then X?=X?(T)=AodS?+(1+r)(Xo-A?So).If X? has a positive probability of being strictly positive, then we must either have X?(H)0 or X(T)0. (i) If Xi(H)0,then △ouS?+(1+r)(Xo- △oSo)0.Plug in Xo=0,we get u △o(1+r) △g. B