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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.
1. Black-Scholes formula.
2. Change of variables for Kolmogorov equation.
3. Mean reverting equation.
4. Affine SDE.
5. Heston equations.
6. Displaced Heston equations.
7. Stochastic volatility.
8. Markovian projection.
9. Hamilton-Jacobi Equations.
A. Characteristics.
B. Hamilton equations.
C. Lagrangian.
D. Connection between Hamiltonian and Lagrangian.
E. Lagrangian for heat equation.
IV. Data Analysis.
V. Implementation tools.
VI. Basic Math II.
VII. Implementation tools II.
VIII. Bibliography
Notation. Index. Contents.

Lagrangian for heat equation.

e proceed to verify that the expression MATH is a Lagrangian for the heat equation MATH MATH

We form the "action" function as follows MATH and calculate the variation MATH hence, MATH Similarly, the calculation of MATH leads to MATH

Unfortunately, general Hamiltonian technique is not applicable to the heat equation because the defining equation for p ( generalized impulse equation ) does not have a solution for q ( generalized impulse solution ).

Notation. Index. Contents.

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