Comment by Maxatar

Profitability is not in any way considered a property of the correctness of an algorithm. An algorithm can be profitable and incorrect, and an algorithm can be correct but not profitable.

Correctness has to do with whether the algorithm performed the intended actions in response to the inputs/events provided to it, nothing more. For the most part correctness of an algorithm can be tested the same way most software is tested, ie. unit tests, but it's also worth testing the algorithm using live data/back testing it since it's not feasible to cover every possible scenario in giant unit tests, but you can get pretty good coverage of a variety of real world scenarios by back testing.