<i>For most people, using these brokers will be something that they will be quite familiar with, even though the actual trading of their shares will happen somewhere in the background. Brokers in fact do not always have to go to an exchange directly, and many will route (send) client orders to various third parties such as market makers or other brokers. This was made quite apparent in 2020 when it was noticed that the broker RobinHood was selling client order flow (client orders) to the hedge fund Citadel.</i><p>Online brokers have been doing this forever. TD Ameritrade is by far the worst offender in this regard, way worse than Robinhood.
> Notice that this method is a lot simpler than the other two, but because you have to use average price, you are exposed to floating point imprecision which is a lack of accuracy that computers have when computing decimals.<p>Using average price and floating point imprecision are two separate, unrelated issues. You don't have to, and probably shouldn't use floating point to calculate the average price, and it's perfectly possible to use decimal arithmetic or fractions rather than floating point.<p>The real issue here is that 2/3 does not have a decimal representation, not floating point imprecision. No matter what you do, if you need to express it as a decimal of finite length it will need to be rounded, and that's where the imprecision is. In practice, you can generally get away with using floats because the floating point error ends up being less than the rounding imprecision.
Question: suppose i bought some security through a broker, and 2 business days have passed. How can i <i>independently</i> (of broker) check that it is indeed now in my name?