The primary function of a Market Maker in the stock exchange is to enhance liquidity by actively placing buy and sell orders for securities, while simultaneously seeking to capitalize on fluctuations in stock prices. In contemporary stock exchanges, most of the trading takes place through computerized systems, thereby necessitating a heightened emphasis on the rapidity and intricacy of transactions. This is accomplished with the broad usage of high-end software and algorithms deployed by Banks, Hedge Funds, Proprietary Trading firms etc. The scope of this thesis is the development, application, and comparative study of Online Training methodologies in the field of market-making applications. To accommodate the inherent variety of approaches to this problem, we begin with a review of relevant parts of the financial field to identify parameters and limitations that will prove significant later. We move on with a review and categorization of algorithmic approaches to identify representative candidate methodologies to compare against. We make an extended presentation of various meta-algorithms, especially Expert and Bandit problem variants, which are useful for challenging data, especially those exhibiting Concept Drift. In the latter chapters of this work, we present a novel approach for Online Training and lay the groundwork for reproducible, comprehensive applications, as well as document and discuss the results. Lastly, we perform comparative research between methodologies, documents, and discuss the results in order to derive insights furthering the field.