The real question is, what does wealth represent. Only when you answer that can you answer what a financial center does.
Dipping into negative wealth represents your civilization overloading its ability to accomplish things. There's not enough people, not enough expertise, too much corruption, and so on and so forth. So financial centers can represent anything that reduces these problems. It could be bureaucrats to keep track of things, taskmaster AIs to direct activity efficiently, replicant facilities so people can double their workload, robot factories to reduce workload, or financial wizards that optimize economic activity. Or whatever else you can imagine.