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

Cox process.

he intensity $\lambda$ may be a random process. It is convenient to restrict attention to situation of independent intensity $\lambda_{t}$ and jumps $\tau $ . In other words, we first simulate $\lambda_{t}$ and then, for given $\lambda_{t}$ , simulate $\tau$ . Such construction is called "Cox process".

Notation. Index. Contents.

Copyright 2007