The market is a controlled dynamic system. - page 348

[Maxim Dmitrievsky]

Aleksey Nikolayev:

"He who knows does not speak; he who speaks does not know". (С)

[[Deleted]]

Let's go back to the beginning so to speak and start from the beginning ;)

Forum on trading, automated trading systems and testing trading strategies

The market is a controlled dynamic system.

Oleg avtomat, 2011.05.21 06:24

So let's start from the beginning.

Open a terminal. Select any instrument. And we get the quotes flow - where from? how? why? From a brokerage company? From nothingness? -- No.) From the market!

And the money tree is growing!

Forum on trading, automated trading systems and trading strategies testing

The market is a controlled dynamic system.

Oleg avtomat, 2011.05.21 06:42

... This is not a very good picture to work with in the future, so I will change it to a more palatable form:

.

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and at once we notice in this picture an autonomous generator.

[[Deleted]]

The "generator" approach is not bad at all:

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(note in brackets that the "generator" approach successfully grinds down any BPs, including SBs)

However, we are now interested in the "game" approach.

[[Deleted]]

This time we will look at the Market not as an autonomous generator, but as a self-organising system:

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Or, closer to the truth, as a hierarchical system with an external goal-setter:

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In either case, only the output S(t) is available for direct observation.

[Younga]

I would love to read it!

[Igor Makanu]

Олег avtomat:

Let's go back to the very beginning, to the beginning, so to speak. And again, let's start from the stove ;)

A lot of criticism in your address, but I'm pleased to read your thread, it has a rationale

But how realistic is it to run simulation in Matlab or VisSim version 5 or 6? (on the Internet they are lying), imho, in specialized programs faster to see the graphical result of mathematical modeling

[[Deleted]]

Younga:
I'd love to read it!

Constructive comments, suggestions, questions, ideas, thoughts are welcome.

[[Deleted]]

Igor Makanu:

A lot of criticism in your address, but I enjoy reading your thread, there is a rationale behind it

But how realistic is it to run the simulation in Matlab or VisSim version 5 or 6? (they are lying on the internet), imho, in specialized programs faster to see graphical results of mathematical modeling

1) There is a lot of criticism. And it happens because of misunderstanding of what I do, which is not consistent with their ideas.

2) These packages are quite suitable for conducting simulations.

[[Deleted]]

Overview.

DIFFERENTIALGAMES

-A section ofmathematicalcontroltheory(seeAutomaticControlTheory)thatstudiescontrolinconflictsituations.The theoryof D.i.isalsoattachedtothegeneralgametheory.The firstworksonD.i.theoryappearedin themid-50sof the20thcentury.

A distinction is made betweentwo-playerandmulti-playerGIs.Mainresults areobtainedforproblemswithtwoplayers.Asubstantivedescriptionof theseproblems can be summarizedinthefollowingscheme.There is adynamicsysteminwhicha part ofcontrolactions is subordinatedto playerI,andanotherpart toplayerII.Whenposinga problemfacedbyplayerIorII,it is assumedthatthisplayer'schoiceof controlsguaranteeinghimattainment of aparticulargoalunder anyunknownbeforehandcontrolof the opponent,canonlybe basedonsomeinformationabout the currentstatesof the system.D.i.theoryalsoconsiderscontrolproblemsinconditions of indeterminacywheninterferenceactingonthe systemis treatedas acontrol ofthe opponent.e.g,Itis usuallyassumedthatthe motion of a controlledsystem isgivenby the differentialequation

wherex isaphasevectorof the system,andv arecontrolvectorsof playersIandIIrespectively.We definea class of strategiesof playerI,andforeachstrategy,we definea bundle ofmotionsX(U)generatedby this

look further

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Overview.

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Averbukh Y.V. "Differential games. Some formulations and results".

Abstract: Differential game theory is a part of mathematical control theory which studies control problems in the case of interaction of several control subjects. In this paper we will focus only on the best studied class of differential games, antagonistic differential games. In this case, we have a system controlled by two entities with opposite goals. Within the framework of the theory of antagonistic differential games, pursuit problems, homing problems in the presence of a disturbance, and holding problems in the set in the presence of a disturbance are formalized. We will consider model problems, issues of strategy class selection and construction of optimal controls. I will also discuss the relation between differential games and first order partial derivative equations.