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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.
IV. Data Analysis.
V. Implementation tools.
1. Finite differences.
2. Gauss-Hermite Integration.
3. Asymptotic expansions.
4. Monte-Carlo.
A. Generation of random samples.
B. Acceleration of convergence.
a. Antithetic variables.
b. Control variate.
c. Importance sampling.
d. Stratified sampling.
C. Longstaff-Schwartz technique.
D. Calculation of sensitivities.
5. Convex Analysis.
VI. Basic Math II.
VII. Implementation tools II.
VIII. Bibliography
Notation. Index. Contents.

Control variate.

et $Z,X,Y$ be some random variables with finite second moments and MATH MATH We assume that $E\left( X\right) $ is known and $X$ is easy to simulate. The $Y$ is the variable of interest for some original problem. We mean to improve speed of convergence by calculating $Z$ instead of $Y$ . We have MATH We are looking for the value of $b$ that delivers the minimum of the above expression. MATH MATH MATH MATH MATH MATH We see that for efficiency of this technique we need an easily simulated variable $X$ that has strong correlation with the variable of interest $Y$ .

Notation. Index. Contents.

Copyright 2007