{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:22:21Z","timestamp":1760145741842,"version":"build-2065373602"},"reference-count":52,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2024,8,28]],"date-time":"2024-08-28T00:00:00Z","timestamp":1724803200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Portuguese funding agency, FCT\u2013Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","award":["LA\/P\/0063\/2020","UIDB\/50014\/2020","PTDC\/MAT-APL\/31753\/2017"],"award-info":[{"award-number":["LA\/P\/0063\/2020","UIDB\/50014\/2020","PTDC\/MAT-APL\/31753\/2017"]}]},{"name":"project \u201cModelling, Dynamics and Games\u201d","award":["LA\/P\/0063\/2020","UIDB\/50014\/2020","PTDC\/MAT-APL\/31753\/2017"],"award-info":[{"award-number":["LA\/P\/0063\/2020","UIDB\/50014\/2020","PTDC\/MAT-APL\/31753\/2017"]}]},{"name":"CMUP\u2013Centro de Matem\u00e1tica da Universidade do Porto","award":["LA\/P\/0063\/2020","UIDB\/50014\/2020","PTDC\/MAT-APL\/31753\/2017"],"award-info":[{"award-number":["LA\/P\/0063\/2020","UIDB\/50014\/2020","PTDC\/MAT-APL\/31753\/2017"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematics"],"abstract":"<jats:p>We model the financial markets as a game and make predictions using Markov chain estimators. We extract the possible patterns displayed by the financial markets, define a game where one of the players is the speculator, whose strategies depend on his\/her risk-to-reward preferences, and the market is the other player, whose strategies are the previously observed patterns. Then, we estimate the market\u2019s mixed probabilities by defining Markov chains and utilizing its transition matrices. Afterwards, we use these probabilities to determine which is the optimal strategy for the speculator. Finally, we apply these models to real-time market data to determine its feasibility. From this, we obtained a model for the financial markets that has a good performance in terms of accuracy and profitability.<\/jats:p>","DOI":"10.3390\/math12172676","type":"journal-article","created":{"date-parts":[[2024,8,28]],"date-time":"2024-08-28T11:54:10Z","timestamp":1724846050000},"page":"2676","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Game Theory for Predicting Stocks\u2019 Closing Prices"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1048-5465","authenticated-orcid":false,"given":"Jo\u00e3o Costa","family":"Freitas","sequence":"first","affiliation":[{"name":"Faculty of Sciences, University of Porto, R Campo Alegre, 4169-007 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2953-6688","authenticated-orcid":false,"given":"Alberto Adrego","family":"Pinto","sequence":"additional","affiliation":[{"name":"Faculty of Sciences, University of Porto, R Campo Alegre, 4169-007 Porto, Portugal"},{"name":"Artificial Intelligence and Decision Support (LIAAD)\u2014Institute for Systems and Computer Engineering, Technology and Science (INESC TEC), University of Porto, R Campo Alegre, 4169-007 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9010-2075","authenticated-orcid":false,"given":"\u00d3scar","family":"Felgueiras","sequence":"additional","affiliation":[{"name":"Faculty of Sciences, University of Porto, R Campo Alegre, 4169-007 Porto, Portugal"},{"name":"Centro de Matem\u00e1tica da Universidade do Porto (CMUP), University of Porto, R Campo Alegre, 4169-007 Porto, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,28]]},"reference":[{"key":"ref_1","unstructured":"(2020, January 23). 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