Quantitative Analysis
Parallel Processing
Numerical Analysis
C++ Multithreading
Python for Excel
Python Utilities
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I. Basic math.
II. Pricing and Hedging.
III. Explicit techniques.
IV. Data Analysis.
V. Implementation tools.
VI. Basic Math II.
1. Real Variable.
2. Laws of large numbers.
3. Characteristic function.
4. Central limit theorem (CLT) II.
5. Random walk.
6. Conditional probability II.
7. Martingales and stopping times.
8. Markov process.
A. Forward and backward propagators.
B. Feller process and semi-group resolvent.
C. Forward and backward generators.
a. Example: backward Kolmogorov generator for diffusion.
b. Example: backward Kolmogorov generator for Ito process with jump.
D. Forward and backward generators for Feller process.
9. Levy process.
10. Weak derivative. Fundamental solution. Calculus of distributions.
11. Functional Analysis.
12. Fourier analysis.
13. Sobolev spaces.
14. Elliptic PDE.
15. Parabolic PDE.
VII. Implementation tools II.
VIII. Bibliography
Notation. Index. Contents.

Example: backward Kolmogorov generator for diffusion.

ur goal is to calculate the operator ( Backward Kolmogorov generator ) for the diffusion process MATH where the $a(t,x)$ and MATH are real-valued functions and $dW_{t}$ is the standard Brownian motion.

By definition ( Backward Kolmogorov generator ), MATH We apply the Ito formula ( Ito_formula ) under the expectation: MATH

Notation. Index. Contents.

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