TL;DR: You can't stop them -- IF they want to dominate.
With about 1% of the population immortal until killed, that is 80,000,000 people out there that aren't dying anytime soon. I sincerely doubt that all 80 million of those people want to rule the world. My presumption that they have similar ambitions as the rest of us.
To compare, Germany has about 83 million people so that might be a good sample size of about 1% of the population. For a bit less then 1% of the world's population, Thailand's 70 million or the UK's 68 million could also work as a cross section.
To dominate economically is not as simple as leaving piles of money in assorted financial institutions to collect interest for a century or three. While that might keep people comfortable provided they have enough money to collect interest on, it is unlikely to help them dominate economically.
Plus, if the institution terminates, there is a good changes that your money goes with it. Or the country holding your money for that matter.
Economic domination is as much about knowing where and when to invest as much as it is about stashing your cash. Today, that might be scouring the internet and newspapers for the current economic news and trends as well as looking up the cutting edge technologies, which is probably a job in itself that you have delegated to qualified staffers.
In the times before easily accessible news, your immortal would likely have to place themselves in a position socially to not only have access to the news, but have access to it in a timely manner so that they can act on it. This likely involves extra expenses in maintaining a higher lifestyle than somebody that is happy living a simpler life.
After all, it is one thing to learn through gossip that one man's copper is of inferior quality, but another to determine why it is inferior. Determining the whys of the situation is also part of the legwork needed -- some it may be delegated to paid informants and helpers, but it is still work that needs to be done. Is it the mine that is faulty, the worker that smelted the ingot, or the mine boss trying to make more money?
Also, your immortal would have to keep an ear out for the political situation in the area. Ideally, they will work to situate themselves as a thoroughly neutral power with a large treasury. While they might not directly rule this neutral country, they will certainly be the power and money behind that throne. Some manner of iron bank perhaps.
Today, it might be easier to dominate as they could buy shares in promising start-ups and reap the cheap rewards. Look at Microsoft and Apple as tech startups back in the days as well as Amazon. As you go back in the decades, there is probably other startups that would have made them a lot of money in the day. Divesting those investments if the company looks to be in serious trouble is also an art in itself. All those profits in buying and selling the stock coupled with the dividends from retained shares does into buying more stock and companies until they dominate.
Plus in this era, it is easier to bribe ... er lobby ... politicians into seeing things your way through expert advice. They will not have an interest in an excessive wealth tax that consistently drains their economic power, nor in any term limits on their wealth. Loopholes will be written into those laws for them to exploit, such as the establishment of corporations.
However, they might be a bit more willing to pay their fair share in some instances seeing that a happy and well taken care of workforce is a more productive one. Provided they don't have pay too much of course.
Also, let's not forget the "until killed" part of their immortality. If you anger the wrong person, there is a good change that an assassination attempt or twelve might be in your future. You could be looking out for knives and poison for decades if you step on too many people on your way up. I could see many cashing out before that happens.
To put this in contrast, take an immortal that has a desire to just live comfortably and not have to worry about working or a lavish lifestyle. They wouldn't need a billion dollars in assets. They could work for a few decades, live off their savings for a few decades while upgrading their skills, then go back to work, repeating the cycle. Sure, they might need to know how to invest their modest savings but they aren't interested in taking over the market -- just investing in it.
So no, I don't think there is a way to prevent an immortal economically dominating an area, or even the world, should they choose to. We can't even keep mortals from doing it now and your immortal potentially has centuries of experience. I just don't think that there would be many that want to.