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目录如下：作者：RobertJ.Elliott P.Ekkehard Kopp
1PricingbyArbitrage1
1.1Introduction:PricingandHedging ..............1
1.2Single-PeriodOptionPricingModels .............9
1.3AGeneralSingle-PeriodModel ................12
1.4ASingle-PeriodBinomialModel ...............13
1.5Multi-PeriodBinomialModels ................17
1.6BoundsonOptionPrices ...................21
2MartingaleMeasures23
2.1AGeneralDiscrete-TimeMarketModel ...........23
2.2Trading Strategies and Arbitrage Opportunities .......25
2.3Martingales and Risk-Neutral Pricing ............30
2.4Arbitrage Pricing with Martingale Measures .........32
2.5Example:Martingale Formulation of the Binomial Market Model..............................35
2.6 From CRR to Black¨CSchole ..................38
3The Fundamental Theoremof Asset Pricing
45
3.1The Separating Hyperplane Theoremin
.........45
3.2Construction of Martingale Measures .............47
3.3A Local Form of the No ArbitrageˉConditi ........49
3.4Two Simple Examples .....................56
3.5Equivalent Martingale Measures for Discrete Market Models ..................59
4Complete Markets and Martingale Representation
63
4.1Uniqueness of the
EMM ....................63
4.2Completeness and Martingale
Representation ........65
4.3Martingale Representation in the CRR-Model ........66
4.4The Splitting Indexand Completeness ............70
4.5Characterisation of Attainable Claims ............73
5Stopping Times and American Options75
5.1Hedging American Claims ...................75
5.2Stopping Times and Stopped Processes ...........77
5.3Uniformly Integrable Martingales ...............80
5.4Optimal Stopping:The Snell Envelope ............86
5.5Pricing and Hedging American Options ...........93
5.6Consumption¨C Investmen tStrategie .............96
6Areview of Continuous-Time Stochastic Calculus99
6.1Continuous-TimeProcesses ..................99
6.2Martingales ...........................103
6.3Stochastic Integrals .......................109
6.4The It o Calculus ........................118
6.5Stochastic Differential Equations ...............126
6.6The Markov Property of Solutionsof SDEs .........130
7European Optionsin Continuous Time135
7.1Dynamics ............................135
7.2Girsanov’sTheore ......................136
7.3Martingale Representation ...................142
7.4Self-Financing Strategies ....................151
7.5An Equivalent Martingale Measure ..............154
7.6TheBlack¨Cscholes Formul ..................163
7.7AMulti-Dimensional Situation ................167
7.8Barrier Options .........................172
8The American Option187
8.1Extended Trading Strategies ..................187
8.2Analysis of American Put Options ..............190
8.3The Perpetual Put Option ...................196
8.4Early Exercise Premium ....................199
8.5Relation to Free Boundary Problems .............202
8.6An Approximate Solution ...................208
9BondsandTermStructure211
9.1Market Dynamics ........................211
9.2Future Price and Futures Contracts .............215
9.3Changing Numerair ......................219
9.4Ageneral Option Pricing Formula ..............222
9.5Term Structure Models ....................227
9.6Diffusion Models for the Short-Term Rate Process .....229
9.7TheHeath¨CJarrow¨CMortonMod ..............242
9.8A Markov Chain Model ....................247
10Consumption-Investment Strategies251
10.1Utility Functions ........................251
10.2Admissible Strategies ......................253
10.3Utility Maximization from Consumption ...........258
10.4Maximization of Terminal Utility ...............263
10.5UtilityMaximization for Both Consumption andTerminal Wealth ......................266
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