The broader OMXS30 index closed up 0.2 percent, and the large-cap OMXS30 index rose 0.4 percent.
At the top of the OMXS30 were truck manufacturer Volvo, which rose 2.2 percent, and heat pump company Nibe, up 2.1 percent.
The worst performers were pharmaceutical giant AstraZeneca and engineering company ABB, down 1.7 and 1.3 percent respectively.
Outside of OMXS30, Apotea plunged almost 22 percent after the online pharmacy company's profit warning on Tuesday.
Before Trump's Davos speech - where he said that the US does not want to use force to take over Greenland - the Stockholm Stock Exchange was down 1.1 percent. The index then turned higher, as did the leading European stock exchanges. However, the DAX index in Frankfurt closed in the red.
The U.S. dollar weakened significantly on the foreign exchange market. At the close of trading, one dollar traded at 9.10 kronor, and the krona also strengthened against several other currencies, including the euro.
With Wednesday's marginal rise, the Stockholm Stock Exchange has now risen 1.7 percent since the turn of the year.
