Afaik the 1/e solution is only optimal when you don't know anything about the distribution being draw from (but also why it's amazing). Since the author knows the probability distribution the prices are being draw from you can do much better with a little dynamic programming.
It's also solving a different problem: it maximises the when probability that you get the absolute best match, rather than maximising the expected value of your choice.
Furthermore, I suspect it requires that each measurement is independent and identically-distributed.
If your measurements are correlated (as prices generally are -- if they were lower than average yesterday, they are more likely to be lower than average today), the secretary-problem approach will not work.
Yes, exactly. I was looking to solve the second problem, not the former. Following the secretary rule is good strategy for a lot of things, but I think we actually have more information here.
