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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.
 A. Example: exponential of stochastic process.
 B. Example: integral of t_dW.
 C. Example: integral of W_dW.
 D. Example: integral of W_dt.
 7 Change of measure.
 8 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.

## Example: exponential of stochastic process.

he goal of this section is to calculate the for where the is a column of deterministic functions of time and is a column of stochastic processes. We have We substitute into the formula ( Ito formula 2 ):

 Notation. Index. Contents.