With the recovery of the first stage on their most recent launch, I was excited and congratulatory, of course. Then my thoughts went forward to the re-use of this launch vehicle.
It would seem that the most clear-eyed assessment of the risk for the re-launch would come from the insurers of that launch. Thus the question: who's been providing the insurance for SpaceX? Are they self-insured? I would think not.
Aon International Space Brokers does, according to this article. Although they likely only cover liability type losses from SpaceX, not the cost of the rocket themselves. In fact, this 2012 FCC document states that SpaceX has 3rd party liability insurance for the first 45 days after a launch, afterward which they are self-insured.
Each payload that is on any rocket tends to be insured to some extent by the payload owner. They may use a variety of insurance providers. These insurance providers will typically review the tests of the satellites and rockets to ensure they are satisfied before agreeing to the launch, and are thus given a seat in making launch decisions.
There are regular insurance markets for satellite launches (i.e. successful delivery to separation), in-orbit satellite operation and third party liability.
There are a number of insurance brokers. Aon, mentioned in PearsonArtPhoto's answer, are one of the larger brokers. They don't take any of the risk but allocate it competitively amongst underwriters. There are about twenty or thirty major underwriters who participate in the asset related insurance for launch and in-orbit and a smaller number that provide third party liability cover.
Almost always the insurance for any one launch is spread over most of the market. The chain of participants does not stop there. For some of the underwriters, their capacity is actually only managed and the risk is borne by other insurers who have placed their trust in them. Furthermore, some underwriters will re-insure a part of their share of the risk.
The insured party in respect of a launch is normally the prospective satellite owner, though it can also be the satellite manufacturer. The insured amount is based on the cost of replacing the satellite and launch.
"It would seem that the most clear-eyed assessment of the risk for the re-launch would come from the insurers of that launch."
It makes sense though insurers are falible too and companies occasionally exit the market due to losses or low returns.
The third party liability market is driven to an extent by regulation. There are varying national obligations on launch service providers and satellite operators, either of whom can be considered the sponsoring party when it comes to third party liability and, correspondingly, can determine which countries are implicated in liability through the Outer Space Treaty and the Liability Convention.
In principle reused launch vehicle stages are little different from new ones in both the launch and liability insurance contexts, they just have a different risk and perceived risk. We'll have to see what happens with the first few reused Falcon 9 first stages though it would make sense that they may be marked up in risk terms to start with until the market gains confidence.
