Quantitative Analysis
Numerical Analysis
C++ Multithreading
Python for Excel
Python Utilities
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I. Basic math.
1. Conditional probability.
2. Normal distribution.
3. Brownian motion.
4. Poisson process.
5. Ito integral.
6. Ito calculus.
7. Change of measure.
A. Definition of the change of measure.
B. Most common application of change of measure.
C. Transformation of SDE under change of measure.
8. Girsanov's theorem.
9. Forward Kolmogorov's equation.
10. Backward Kolmogorov's equation.
11. Optimal control, Bellman equation, Dynamic programming.
II. Pricing and Hedging.
III. Explicit techniques.
IV. Data Analysis.
V. Implementation tools.
VI. Basic Math II.
VII. Implementation tools II.
VIII. Bibliography
Notation. Index. Contents.

Change of measure.


escription of the world may be equiped with more then one probability measure. Hence, the standard Brownian motion under some probability measure may gain a drift after switching to a different probabilistic setup. Thus, by changing probability we control the SDE representation of a given Ito process.

The reference for this section is [Mercurio] .




A. Definition of the change of measure.
B. Most common application of change of measure.
C. Transformation of SDE under change of measure.

Notation. Index. Contents.


















Copyright 2007