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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 Ito process with jump.

e use technique of the previous section to calculate the operator ( Backward Kolmogorov generator ) for the process MATH where the Poisson process $dN_{t}$ has the intensity MATH and $dN_{t}$ is conditionally independent from $dW_{t}$ .

Similarly to the previous section, MATH In order to calculate the above expectation we use the recipe ( Total_probability_rule ). We consider the disjoint events $C_{0}=\{$ the process $N_{t}$ does not jump during MATH , $C_{1}=\{$ the process $N_{t}$ jumps once during MATH and MATH . MATH . MATH According to the chapter ( Poisson process ), MATH By the conditional independence of $dN_{t}$ and $dW_{t}$ , the diffusion terms MATH in MATH are small compared to the jump MATH and do not survive the procedure MATH . Hence, MATH In addition, MATH Consequently, MATH The above results agrees with the section ( Backward_equation_for_jump_diffusion ).

Notation. Index. Contents.

Copyright 2007