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Quantitative Analysis
Parallel Processing
Numerical Analysis
C++ Multithreading
Python for Excel
Python Utilities
Printable PDF file
I. Basic math.
1. Conditional probability.
2. Normal distribution.
3. Brownian motion.
A. Definition of standard Brownian motion.
B. Brownian motion passing through gates.
C. Reflection principle.
D. Brownian motion hitting a barrier.
4. Poisson process.
5. Ito integral.
6. Ito calculus.
7. 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.

Brownian motion passing through gates.

ur goal is to calculate the quantity MATH for the standard Brownian motion $W_{t}$ , some intervals MATH and time moments $t_{1},t_{2}$ , $\ 0<t_{1}<t_{2}$ . The $P$ is probability.

We split the interval MATH into a disjoint union of intervals MATH , MATH . We calculate MATH MATH We use the formula ( Bayes formula ). MATH We make MATH small. MATH MATH We use the formula ( Brownian motion ). MATH MATH MATH We make the change $y\rightarrow z$ , $y=z-x$ . MATH

Notation. Index. Contents.

Copyright 2007