Concept of Martingale in random Processes: from Game system to financial Mathematics

Abstract

The proposed study undertakes an interdisciplinary analysis of the problem of randomness in various forms of social activity. The authors find a significant relation between linguistic analysis and the conclusions of financial mathematics about the possibility of forecasting under conditions of uncertainty. It realizes the intention to find a strategy for profitable actions in random processes. This intention is reflected in the meaning of the concept “martingale”. For centuries it was used to refer to the special capabilities of horse harnesses. Then this term began to denote winning strategies in various gambling games, leading to the enrichment of the one who owns them. The introduction of mathematical calculations into these strategies became one of the foundations of probability theory. In the middle of the last century, the term “martingale” began to denote the process of capital accumulation when implementing a trading strategy in the financial market. In recent years, the concept of martingale began to characterize calculated strategies for playing in the financial market. This opened up the possibility of forming a version of probability theory specially adapted for modeling market phenomena and processes. The emergence of the science of quantum computing and the emergence of new computing capabilities revives the problem of overcoming uncertainty using the means of modern digitalization. Therefore, the concept of martingale, which implies the search for opportunities to control random processes, remains relevant not only for modern economic thought, but also for various areas of social and humanitarian knowledge. Analysis of the nature of randomness and its various manifestations is also relevant for everyday life of modern people.This makes it relevant for educational programs aimed at promoting economic and financial literacy among the population.