This paper aims at clarifying the conditions under which financial globalization originates welfare gains in a simple endogenous growth setting. We focus on the capital-deepening effect of financial globalization in an open-economy AK model and we show that constrained borrowing triggers substantial welfare gains, even at small levels of international financial integration, provided that the autarkic growth rate is larger than the world interest rate. Such conditional welfare benefits boosted by stronger growth - long-run gain - arise in our preferred model without investment commitment, which turns out to be a candidate to solve the "allocation puzzle". For reasonable parameter values and relative to autarky, welfare gains range in our preferred model from about 2% in middle-income countries to about 13% in OECD-type countries under international financial integration. Sizeable benefits emerge despite the fact that consumption falls - short-run pain - and that welfare-reducing growth breaks materialize when the economy switches from autarky to financial integration, which is however shown not to dwarf positive welfare changes.