The issue I see is there's no avoiding putting your trust in the centralized issuer. You can issue and trade inherently centralized assets on a global ledger, but why? What is the advantage for the common man?
I guess the benefit is that you only have to trust the issuer one time. Once the stock has been issued on the blockchain it cannot be manipulated. With a centralized system you'd have to trust the issuer/exchange on an ongoing basis. Whether this difference matters is kind of a philosophical litmus test that divides the blockchain and non-blockchain (i.e. Ripple/Stellar/OpenTransactions) camps.
The exchange would be based on the counterparty protocol, which allows anyone with a BTC address to issue and back assets in a decentralized manner. We'll have to see how this decentralization leaks into what it means to be a stock exchange.