If one makes a certain agreement in business with a non-jew outside the range of something forbidden by the Torah itself (e.g to do something at a certain time or location etc.), is one obliged to honor it?
Let's assume there were no oaths involved, simply a statement like "I will invest." Shulchan Aruch Choshen Misphat 204,7 spells out that if you commit to buy or sell, "you really should keep your word, and if you don't do so, shame on you for your lack of integrity; but the courts can't extract anything from you."
Rabbi Moshe Feinstein writes in Igros Moshe Choshen Mishpat 1,58 that if you commit to a labor union (and he continues on the next page to include even a non-Jewish one) to go on strike when they do, that commitment isn't a buy/sell one, so we don't call it "shame on you for lack of integrity", but we apply the Gemara's comment about how Rav Safra carried through on his mental note to sell to a non-Jew at a certain price. He therefore says honoring your word is "the appropriate thing to do for any truly religious person."
So it's definitely a very strong "should." And there appears to be no distinction whether the counterparty is Jewish or not.
The Beth Din of America got a case involving a verbal agreement in a business setting (something about becoming partners in a pizza store); they ruled "you really should go through with your word, but we can't force you to pay anything." However each sides paid their own legal fees, as really should is enough to make the claim not ridiculous.