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Quantitative Analysis
Parallel Processing
Numerical Analysis
C++ Multithreading
Python for Excel
Python Utilities
Services
Author
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I. Basic math.
1. Conditional probability.
2. Normal distribution.
3. Brownian motion.
4. Poisson process.
5. Ito integral.
6. Ito calculus.
7. Change of measure.
8. Girsanov's theorem.
A. Change of measure-based verification of Girsanov's theorem statement.
B. Direct proof of Girsanov's theorem.
9. Forward Kolmogorov's equation.
10. Backward Kolmogorov's equation.
11. Optimal control, Bellman equation, Dynamic programming.
II. Pricing and Hedging.
III. Explicit techniques.
IV. Data Analysis.
V. Implementation tools.
VI. Basic Math II.
VII. Implementation tools II.
VIII. Bibliography
Notation. Index. Contents.

Girsanov's theorem.


n this section we obtain the inverse result to the statement ( Transformation of SDE under change of measure ). Suppose $W_{t}$ is a standard Brownian motion adapted to a filtration $\QTR{cal}{F}_{t}$ and the process $B_{t}$ is given by MATH where $\theta_{s}$ is some $\QTR{cal}{F}_{t}$ -adapted process. We wish to find a process $h_{t}$ , such that the $B_{t}$ is a standard Brownian motion with respect to the MATH defined according to the formula ( Definition of change of measure ).




A. Change of measure-based verification of Girsanov's theorem statement.
B. Direct proof of Girsanov's theorem.

Notation. Index. Contents.


















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