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Quantitative Analysis
Parallel Processing
Numerical Analysis
C++ Multithreading
Python for Excel
Python Utilities
Services
Author
Printable PDF file
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.
8. Girsanov's theorem.
9. Forward Kolmogorov's equation.
10. Backward Kolmogorov's equation.
11. Optimal control, Bellman equation, Dynamic programming.
A. Deterministic optimal control problem.
B. Stochastic optimal control problem.
C. Optimal stopping time problem. Free boundary problem.
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.

Deterministic optimal control problem.


e assume everywhere that all the functions are regular enough to differentiate and solutions of ODEs exist.

Proposition

Assume existence of solution MATH , MATH of the ODE MATH for some function MATH and a family of functions MATH , MATH . The function MATH satisfies MATH

Proof

We use the short notation MATH , $s\geq t$ . By definition of $u$ , MATH Note that MATH . MATH Hence, MATH

Proposition

Assume that function MATH satisfies the relationships MATH and function MATH is defined by MATH for a fixed $\alpha$ .

Then MATH for any $t$ .

Proof

We calculate MATH MATH MATH Hence, MATH or MATH Note that MATH . Hence, MATH





Notation. Index. Contents.


















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