I. Basic math.
 1 Conditional probability.
 2 Normal distribution.
 3 Brownian motion.
 4 Poisson process.
 A. Definition of Poisson process.
 B. Distribution of Poisson process.
 C. Poisson stopping time.
 D. Arrival of k-th Poisson jump. Gamma distribution.
 E. Cox process.
 5 Ito integral.
 6 Ito calculus.
 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.

## Poisson stopping time.

he random quantity is the arrival of the first jump. We would like to compute the number for some smooth function using the result ( Poisson property 2 ). We replace the notation with " " and proceed as follows Observe that Hence, Therefore, We conclude

 Notation. Index. Contents.