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 described in the section ( Girsanov's theorem ). The process is given by the SDE in "the original measure" (see the section ( Change of measure recipe) ). The should look like a standard Brownian motion under a new measure given by the formula ( Definition of change of measure ) with . We restate the result ( Change of Brownian motion ): Hence the drift is, in fact, the volatility of : We integrate for and conclude Note the correct normalization and the property

 Notation. Index. Contents.