Quantitative Analysis.
Trading Platform.
Python for Excel.
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.
Bibliography.
Forum Notation Index Contents

Deterministic optimal control problem.

otation

MATH where the MATH is an optimal control strategy.MATH

Proposition

The MATH satisfies MATH

Proof

By definition,MATHMATHMATHMATHMATH Hence,MATHMATHMATH

Proposition

Assume that MATH satisfies the relationshipsMATH and the function MATH is defined byMATH for some strategy $\alpha$ thenMATH for any $t$ and the ODE solution $x\left( t\right) $.

Proof

MATHMATHMATH Hence,MATH orMATH The LHS is MATH.





Forum Notation Index Contents


















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