Strategy notes on the quant math behind this Deutsche Bank Forex FX and commodity trading strategy

Here are ny strategy ‘special’ notes thus far on this strategy:

These are just introductory as I dig deeper understanding the relationship of all this data. A lot of it is based on ‘measurement theory’ which is something I have never seen before but could be useful for market forecasting. It is a form schochastic calculus where some say it is useless. I cannot judge as I am new to this. This stuff is based around my the Deutsche Bank FX strategy listed here: https://quantlabs.net/blog/?s=deutsche

Note that these notes are a running list as I learn how to implement and could be wrong as I proceed.

THEORY 2

Is sigmav not the same as traditional theta found in trigonmetry? I assume yes so need to calculate as curve is generated. If so, calculate theta angle no different as explained in http://www.mathsisfun.com/algebra/trig-finding-angle-right-triangle.html

NOTE: Tau is defined as the switch point/change point where the regime STATE switches between up, down, and sideways. See figure 2 pg 13.

s is also the time point between 0 and t that decides the switching regime

THEORY 3

Girsanov theory explained here with measurement theory:

http://www.quora.com/Probability/How-does-one-explain-what-change-of-measure-is-in-Girsanovs-Theorem

Better: http://numericalmethod.com/blog/2013/05/16/change-of-measuregirsanovs-theorem-explained/

To remove the mean, µ, of a Brownian motion, we define

***This is best explained in the link above. As referred to the image of http://en.wikipedia.org/wiki/File:Girsanov.png, we are calculating different paths of the random processes,

Note relationsship of

For a 0 drift process, hence no increment, the expectation of the future value of the process is the same as the current value (a laymen way of saying that the process is a martingale.)

Also refer to http://www.math.nyu.edu/faculty/goodman/teaching/StochCalc2012/notes/Week10.pdf

THEORY 4

For Ito’s theory process (Theory 4),

Martingdale as Stochastic process in which the expected value of an observation (which is conditional on all previous observations) at any stage is equal to the last of the previous observations.

Read more: http://www.businessdictionary.com/definition/Martingdale.html#ixzz3D2FGoGGC

–> Use crossvalind Generate cross-validation indice

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