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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.
a. Uniform [0,1] random variable.
b. Inverting cumulative distribution.
c. Accept/reject procedure.
d. Normal distribution. Box-Muller procedure.
e. Gibbs sampler.
B. Acceleration of convergence.
C. Longstaff-Schwartz technique.
D. Calculation of sensitivities.
5. Convex Analysis.
VI. Basic Math II.
VII. Implementation tools II.
VIII. Bibliography
Notation. Index. Contents.

Accept/reject procedure.


The variables $X$ and $Y$ are given by the distributions MATH and MATH with common support. Assume that MATH We generate the variable $X$ as follows:

Step 1. Generate $\eta$ and $Y$ independently.

Step 2. If MATH then set $X=Y$ otherwise return to step 1.


Indeed, MATH MATH MATH MATH It is a part of the above computation that MATH Hence, for the procedure to be effective, $M$ has to be large.

Notation. Index. Contents.

Copyright 2007