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This work addressed the use of the geometric Brownian motion to simulate theprices of shares listed in the Small Caps index of the Brazilian stock exchangeB3 (Brazil, Bolsa, Balc\~ao). The data used refer to the price history fromJanuary 2016 to December 2018. The price history of 2019 was used to becompared with the simulated prices. The data was imported from the YahooFinance database using the Python programming language, and the simulationswere performed for each stock individually, and for portfolios formed based onexpected returns, risk and the Sharpe Index. The results were better forportfolios with higher returns, lower risks and higher Sharpe Indexes.

Aplica\c{c}\~ao do Movimento Browniano Geom\'etrico para Simula\c{c}\~ao de Pre\c{c}os de A\c{c}\~oes do \'Indice Brasileiro de Small Caps