Quantitative Analysis
Parallel Processing
Numerical Analysis
C++ Multithreading
Python for Excel
Python Utilities
Services
Author
Printable PDF file
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 $\tau$ is the arrival of the first jump. We would like to compute the number MATH for some smooth function MATH using the result ( Poisson property 2 ). We replace the MATH notation with " $\approx$ " and proceed as follows MATH Observe that MATH Hence, MATH Therefore, MATH We conclude MATH





Notation. Index. Contents.


















Copyright 2007