the ones who control most bitcoins has more to lose.
Miners aren't necessarily the ones who control most bitcoins! The early adopters control a large amount, the future miners have less than one-third of bitcoins left to mine the rest of this century.
"Controlling most of bitcoins" and "controlling Bitcoin" are two totally different things. Satoshi, for instance, controls around a million BTC, but he doesn't control Bitcoin's day-to-day functioning any more than the guy with .01 BTC, the miners do tho. They stop -- no more Bitcoin. That's why the halvening is going to be so interesting: either the price of BTC has to spontaneously double, or roughly half of the miners have to close up shop.
I think the halving is already calculated in by the miners in their estimate for their profit. So shortly the hash rate may not go up much, or even down a bit, but after that it will just continue up again. I see no reason to instantly double the value, just like that didn't happen at the previous halving.
It doesn't matter what the miners estimated, one of two things has to [eventually] happen:
1. Bitcoin price must double (so the miners will continue being as profitable at 12.5 coins as they were at 25)
2. Hash rate must halve (so that the remaining miners will be just as likely to solve two 12.5BTC blocks as they were to solve one 25BTC block).
This doesn't need to be spontaneous, some large miners may continue mining at a loss, in hopes that their competitors will go broke and fold first, but eventually nothing other than some combination of (1) and (2) is possible.