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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.
a. Finite difference schemes for heat equation.
b. Stability of one-dim heat equation schemes.
c. Remark on stability of financial problems.
d. Lagrangian coordinate technique.
e. Factorization procedure for 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.

One dimensional heat equation.


he traditional heat equation from physics has the form MATH The financial PDEs come from backward Kolmogorov's equation that has the form MATH for the standard Brownian motion. Note the change in sign in front of the derivatives and the change of the initial condition to the final condition. These two variations effectively cancel in a sense that the nature of the problem is exactly the same.




a. Finite difference schemes for heat equation.
b. Stability of one-dim heat equation schemes.
c. Remark on stability of financial problems.
d. Lagrangian coordinate technique.
e. Factorization procedure for heat equation.

Notation. Index. Contents.


















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