Towards developing a manner of a mathematical approach, even in developing a simple bread-and-butter kind of trading methodology, broadly as to apply any single Technical Analysis system in a systematic trading model, I believe it may be primarily of interest as towards a sense of minimizing risk in open positions on the market, with a manner of a mathematically informed approach to the market data itself.
Candidly, I don’t personally believe I would ever wish to so much as propose to develop any kind of a completely autonomous mechanical or algorithmic trading system. Certainly, I am interested in minimizing the time I should need to spend in studying the market data when developing a strategy for opening positions on the market. I would not wish to believe as though any single mechanical trading platform could run forever unattended, though. Certainly, I’ve read a little about VPS hosting for algorithmic trading systems. As my being - albeit, in a manner, informally so - a student of free/open source applications of UNIX operating systems, in seeing the VPS options that I’ve seen notices about, it reminds me of a broader topic of Wide-Area Networks, candidly - a mechanically simple topic, but fairly a hairy thing to design in any manner of short instant. I understand that a VPS system, ideally, could permit for a certain mobility when tracking one’s open positions on the market. However, I know that it is a matter that may not be without risks, cautions, and serious technical considerations as may naturally attend with any design of an application of such technology. I believe that it is semantically towards a broader sense of [I]computer business systems[/I] - however independently applied, such a manner of CBS.
Of course, I should wish to have developed a system I would believe I can trust, ethically and technically before ever permitting such a thing to mechanically open any manner of market positions for me, in any measure of real currency capital. Thus, I believe such a thing should need a lot of testing, also a fair amount of documentation about the testing methods, and primarily, a lot of documentation as to its design.
I believe that I know at least a little bit of some of the mathematics, if only from a level of a formal High School mathematics studentiship, some couple of years ago. Statistics was not a topic that the courses had covered at depth, but it was a topic that the courses had addressed - so far as of simple applications of set-wise permutations and combinations, at least. Of course, outside of the observation that the time-series data of a financial chart may be relevant in a sense of statistical, if not expressly stochastic analysis: There may be a manner of a logical side to the system of a mechanical trading system, itself.
Towards that end, I’ve found a book that I believe may serve as a helpful, mathematically canonical reference. The text of the book is avaialble at Safari Books Onilne, moreover: Sigaud, Olivier, and Olivier Buffet, eds. [I]Markov Decision Processes in Artificial Intelligence: MDPs, beyond MDPs and Applications[/I]. London: ISTE ; Hoboken, NJ : Wiley, 2010. (Bibliography created with Zotero) I believe that the book’s Chapter 7 may be particularly relevant to the topic of mechanical trading - viz a viz the [I]open system[/I] nature of a mechanical trading system applied onto any manner of realtime market data - certainly not without the canonical material addressed of the book’s Chapter 1, such that may be applicable as towards more of a manner of a closed system - as in which all states of the hypothetical [I]finite state machine[/I] would be controlled internally of the closed system, itself. Of course, a realtime market data stream may not be so simple to make decisions about - whether of a personal investor, or for a proverbial software-based investor - as a market being, logically, an open system.
Broadly, the text describes some kinds of essentially logical models developed for applications in mechanical decision-making systems. The book’s title denotes a concept of AI, thus, as a concept. However, with regards to so many mathematical models as are described in the book, I believe that it may serve to find an application in any arbitrary number of a computational methodologies as may be applied for any manner of ethically viable process automation onto stochastic systems - including, in any system for mechanical trading onto time-series market data in a realtime investments market.
So, I’m afraid it’s not an easy topic to breeze through, but it seems that there are some existing works in academia.