Private Equity on Mars

So firstly, Musk did also note that many people would die on his little fun pursuits. I think it will be a while until humanity is in a position for extra-terrestrial financing. Nonetheless, I'll try to provide a half-decent answer. 

One big problem with Mars is the lack of anything particularly valuable to send back to Earth (or to use as rocket fuel for missions deeper into the universe, so-called in-situ resource utilisation). In this respect, the Moon is much more attractive and several stakeholders - from governments (US/Luxembourg/UAE) to the private sector - are starting to try and work out how the legal property rights would need to be implemented. The legal situation is a complete mess right now and it is not clear if private sector firms can actually own any land - under international space law, they probably should not, but it's far from explicit. There is a not insignificant chance that the private sector - including finance - will never really be able to operate extra-terrestrially or at best it will be "world state permits" for resource extraction.  

So before more complex financing gets sorted out, property rights for the private sector would need to be settled. If we can move beyond a primitive colony, then I'm not sure why finance wouldn't grow much like it has on Earth? Given what would need to happen to the place, it would be paradise for early stage venture capital investing... although much depends on how much wealth gets moved (or even if they use the same currencies). I would also say that over the next couple of decades there's a huge amount of ridiculously high risk, ridiculously high potential return opportunities in this space - various mining/fuel opportunities both to bring back to Earth and to use in-situ (helium 3, platinum, rare earths, water/lunar propellent, etc.), significant telecomms opportunities IF colonies are established, and a massive commercial race to put private sector satellites up. Luxembourg is probably the place to be for this; the US sector is mostly concentrated in a few big, more well-established companies.