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Stochastic Calculus for Finance II:
Continuous-Time Models
Solution of Exercise Problems
Yan Zeng
Version 1.0.8, last revised on 2015-03-13.
Abstract
This is a solution manual for Shreve [14]. If you find any typos/errors or have any comments, please
email me at zypublic@. This version skips Exercise 7.1, 7.2, 7.5–7.9.
Contents
1 General Probability Theory 2
2 Information and Conditioning 10
3 Brownian Motion 16
4 Stochastic Calculus 26
5 Risk-Neutral Pricing 44
6 Connections with Partial Differential Equations 54
7 Exotic Options 65
8 American Derivative Securities 67
9 Change of Numéraire 72
10 Term-Structure Models 78
11 Introduction to Jump Processes 94
1
1 General Probability Theory
⋆ Comments:
Example 1.1.4 of the textbook illustrates the paradigm of extending probability measure from a -algebra
consisting of finitely many elements to a -algebra consisting of infinitely many elements. This procedure is
typical of constructing probability measures and its validity is
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