Actually, risk-aversity is very basic to older philosophies and there is a strong trend against it as those philosophies mature. So it has vast and broad support, but is resisted more and more as we move forward. It is ambiguous whether there are any arguments in its favor that do not then have more powerful contradictions later.
Epicureanism favors the lack of fear resulting from removing risk as a separate, special category of good -- the katastemic or static pleasure. Economics and Utilitarianism, Epicurus' more modern form, tends to reject affording absolute good to the sustainable state, and seeks to characterize it in terms of some dynamic tension between risk and reward.
The Stoics strongly valued avoiding premature closure, and taking a risk is the most common stereotype for allowing premature closure, as they reached their epitome in Skepticism, they took avoidance of attachment to an outcome as a principle value. Their revival in modern skepticism that leads us through Nietzsche, strongly attacks cowardice and conformity as the ultimately greater risk, putting risk avoidance into a state of complete paradox.
Schools like Cynicism and those attending to Heraclitus, who promote risk as a natural part of every aspect of life, which is to be embraced, rather than controlled fare very badly historically, but will not die. They often are resurrected and reshaped in positive directions in the thinking of those who move us forward later. Dialecticism takes this notion of basic instability, and gives it a reason, but encourages sustaining it, if not pushing it toward less stability.
Modern moves in psychology toward a 'therapeutic' direction may be taken as a return to pursuit of stability and limitation of risk. But it is not a strong thread. Also people motivated by the destructiveness of the Western lifestyle are preaching sustainability once more, and speaking in terms of risk-aversity and empathy for the future. So this trend away from safety as a value in itself is not absolute, but it remains strong.