Source: John Sellars, Stoicism (Berkeley: University of California Press, 2006) 126.
"But of course every finite being will come up against external causes that will limit its freedom. Ideally one will want to reduce the number of those freedom-limiting encounters and to reduce the impact that they have when they occur. One way of achieving this is to reduce one's reliance on external goods. If one's happiness depends solely on one's virtue, as Stoicism argues that it should, then one will become immune to a whole range of external causes that would otherwise create adverse affects, such as the thief who takes your wallet, for instance."
I read this quote as if it offers an explanation for Stoic asceticism. Maybe I'm reading too much into it--I don't know. I interpreted it to mean that, if one doesn't have too many external goods to worry about, then one won't become overly attached to them, and there won't be any disappointments when they end up being unreliable.
That could be, but it sounds rather escapist. Shouldn't a strong Stoic be able to enjoy the world's goods, without going berserk if they end up disappointing him? Paul said in Philippians 4:11-13 that he learned to be content with much and with little, since Christ is the source of his strength in both situations. Paul didn't have to possess much or little to be content.
Paul here says that it's possible for a Christian to have much, but there are other places in the New Testament and early Christian literature that are more anti-wealth. Jesus often warns against trusting the riches of this world, encouraging his disciples to look for treasures in heaven instead (e.g., Matthew 6:19-21). He also exhorts them to sell their possessions and give alms (Luke 12:33).
Similarly, in Barnabas and Clement, there is a sense that believers should give away their riches. The Shepherd of Hermas, however, doesn't seem to oppose wealth, but it recognizes that preoccupation with riches can divert one's attention from spiritual pursuits. Under this rationale, a rich Christian can keep on being rich, as long as he spends time with God and gives some of his wealth to the needy.
Somehow, we need to find a way to appreciate the good things that we have, without becoming overly attached to them, selfish, and less focused on more important things. Some Stoics seem to have assumed that it's best to bypass that whole dilemma. And maybe that's all right. Different people have different vulnerabilities to temptation.