Quantitative Analysis
Parallel Processing
Numerical Analysis
C++ Multithreading
Python for Excel
Python Utilities
Printable PDF file
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.

Change of measure-based verification of Girsanov's theorem statement.

e would like to calculate the $h_{t}$ described in the section ( Girsanov's theorem ). The process $B_{t}$ is given by the SDE MATH in "the original measure" (see the section ( Change of measure recipe) ). The $B_{t}$ should look like a standard Brownian motion under a new measure given by the formula ( Definition of change of measure ) with $a_{t}:=h_{t}$ . We restate the result ( Change of Brownian motion ): MATH Hence the drift $\theta_{t}$ is, in fact, the volatility of $h$ : MATH We integrate for $h_{t}:$ MATH and conclude MATH Note the correct normalization MATH and the property MATH

Notation. Index. Contents.

Copyright 2007