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Quantitative Analysis
Parallel Processing
Numerical Analysis
C++ Multithreading
Python for Excel
Python Utilities
Services
Author
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I. Basic math.
II. Pricing and Hedging.
III. Explicit techniques.
IV. Data Analysis.
V. Implementation tools.
1. Finite differences.
A. Finite difference basics.
B. One dimensional heat equation.
C. Two dimensional heat equation.
D. General techniques for reduction of dimensionality.
a. Stabilization.
b. Predictor-corrector.
c. Separation of variables for Crank-Nicolson scheme.
E. Time dependent case.
2. Gauss-Hermite Integration.
3. Asymptotic expansions.
4. Monte-Carlo.
5. Convex Analysis.
VI. Basic Math II.
VII. Implementation tools II.
VIII. Bibliography
Notation. Index. Contents.

General techniques for reduction of dimensionality.


e seek to improve efficiency of the finite difference scheme by splitting the spacial operator $A$ into some positive components $A=A_{1}+A_{2}$ and replacing the inversion of $A$ with consecutive inversions of $A_{1}$ and $A_{2}$ . In this section we always assume that some original scheme already has stability and approximation properties and we show how to separate operator while keeping these properties.




a. Stabilization.
b. Predictor-corrector.
c. Separation of variables for Crank-Nicolson scheme.

Notation. Index. Contents.


















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