Quantitative Analysis
Parallel Processing
Numerical Analysis
C++ Multithreading
Python for Excel
Python Utilities
Printable PDF file
I. Basic math.
II. Pricing and Hedging.
III. Explicit techniques.
IV. Data Analysis.
V. Implementation tools.
1. Finite differences.
A. Finite difference basics.
a. Definitions and main convergence theorem.
b. Approximations of basic operators.
c. Stability of general evolution equation.
d. Spectral analysis of finite difference Laplacian.
B. One dimensional heat equation.
C. Two dimensional heat equation.
D. General techniques for reduction of dimensionality.
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.

Approximations of basic operators.

e consider approximation on the uniform lattice with the step $h$ . We introduce the following notations MATH MATH MATH MATH MATH MATH MATH Verification of the following results is the direct application of the Taylor's formula. MATH MATH MATH MATH If a global lattice has been introduced and the MATH is a function defined on the lattice then we use the notation MATH MATH and so fourth. The general statements (for any $k$ ) may be written with the $k$ suppressed: MATH

Notation. Index. Contents.

Copyright 2007