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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.
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.

Hamilton-Jacobi Equations.


he reference for most of material here is [Evans] .

The main result of this chapter is negative: even though there is a Lagrangian for the heat equation nevertheless the Hamiltonian technique does not apply. However, the method of characteristics is separately useful.

We are considering a PDE of the form

MATH (First order PDE)
where the $u$ is an unknown function MATH , the variables $x$ are from $R^{N}$ , the $\partial u$ refers to the vector of derivatives MATH and the function $F$ is smooth. We will use the following notation for the function $F$ 's arguments: MATH




A. Characteristics.
B. Hamilton equations.
C. Lagrangian.
D. Connection between Hamiltonian and Lagrangian.
E. Lagrangian for heat equation.

Notation. Index. Contents.


















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