Multisig + nLockTime transactions could do the job. First, we guarantee that the service operator is not able of running away with the money. With nLockTime we guarantee that, even if the operator disappears, the money shall come back to its rightful owners in, say, one month. I guess similar things could be implemented in OT to give the same guarantees concerning the assets.
Obviously, there's a long road to get there. nLockTime is currently not fully supported by the network. AFAIK BitcoinJS doesn't do multisig, and I know no other javascript client that could be easily embedded in a browser. I don't know if OT currently supports multisignature either, nor if there is a javascript OT client. Being honest, multisig isn't really essential. But multisig may also protect the user against a malware in their own computer. I find this important.
There's still an important trust issue that remains unsolved: the asset issuers. Established companies might not dare openly selling their shares in a black market. Actually, I wonder if any non-anonymous company would. And as we know already, trusting an anonymous issuer is a serious issue. There might be ways to overcome this problem too, but it won't be simple.
You can't trust an anonymous issuer, never ever. Somebody might say he needs some money to expand his mining farm and in reality the money goes to the Mafia. They can make up any bullshit that somebody might believe and there's no way to verify it. They might pay interest every week and even if you don't lose any money there's every likelihood that your money will be used for some nefarious purpose instead of what they told you. No thanks.