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.
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.


ote that for any pair of operators $A_{1}$ and $A_{2}$ we can write MATH Hence, the scheme MATH is equivalent to the Crank-Nicolson MATH after grouping some $\tau^{2}$ -order terms. Therefore, if Crank-Nicolson approximates with second order then so does the scheme (*).


The scheme $(\ast)$ preserves stability.


Make the change of function MATH then MATH MATH or MATH where MATH by the Kelly theorem because $A_{i}\geq0.$

To transform the scheme (*) into a calculation recipe observe that MATH MATH MATH We conclude MATH Hence, we replaced inversion of MATH with consecutive inversions MATH and MATH .

Notation. Index. Contents.

Copyright 2007