Hochschule Düsseldorf
University of Applied Sciences
Fachbereich Medien
Faculty of Media

ISSN: 2567-2347

editor-in-chief: Peter Vogel, peter.vogel@hs-duesseldorf.de

staff-member: Patrick Blättermann, patrick.blaettermann@hs-duesseldorf.de

The series TRADING, founded on July, 2017, covers scientific reports about algorithmic trading.
This includes, for example, the topics investing, order execution and evaluation of stock price data.
The series intends to bridge the gap between theory and practice, reporting scientific results without secretiveness and giving new insights.
Technical terms are kept to a minimum in order to reach a broader readership.

Trading 1: Investing as Random Trial

An investment algorithm is introduced for a market of individual securities by maximizing the amount of investment for each trading day.

This is done under constraints in order to limit the risk and trading costs and to take into account an individual investor.
Purchased securities are selected randomly among those who meet the buy condition, making trading a RANDOM TRIAL.
The expected return is evaluated for the investment algorithm with respect to the random selection for a holding period of one day, i.e. securities are sold after one trading day.

(short abstract)


Trading 2: Ideal Trading

The product formula describing the expected return in no.1 is extended to holding periods longer than one day.
In a first step, the trading period is divided into segments, each comprising a fixed number of subsequent trading days, given by the holding period, and the capital at the end of each segment is described analytically.
In a next step, the concept of IDEAL TRADING is introduced.
One of its idealizations is its non-causality.
This concept enables a product formula, which can be evaluated non-recursively and for various buy conditions simultaneously, as for a holding period of one day.