Does pilot monitoring have authority to go around in exceptional circumstances? Let's say the captain is acting as the pilot flying(PF) and the first officer the pilot monitoring(PM) in a commercial jet. They are shooting an ILS to their destination airport but the approach is so unstable that the first officer shouts "go around, go around" after passing minimum. But the captain ignores him and wouldn't balk the landing.

In this situation, does the first officer have the authority to take the controls from the captain by shouting "my controls" and go around? What about if their roles are switched? That is, what if the captain was the PM and the first officer the PF? Is the captain allowed to overide the first officer's decision to continue and initiate a go-around? I think this question can be better answered by commercial or airline pilots because I believe this is determined by company SOPs rather than FAR or ICAO rules. If so, are there any airlines that render the PM the authority to go around in defiance of the PF's decision under certain circumstances, like when the PM firmly believes the plane will very likely crash if an immediate balked landing is not initiated?
The captain is the captain, so when he says "go around" then the PF needs to initiate the go-around.  If the FO doesn't initiate the go-around as directed, then the captain can (at that time as at essentially any other time he sees it necessary) take over control of the aircraft.  That's the captain's authority and it's pretty clear.

The other case is slightly less clear, but only slightly.

Most operations probably have a directive along the lines that the PF is required to go around when the PM so directs.  So if the captain is flying and the FO directs a go-around, what the captain/PF should do is perfectly clear.  If he doesn't do so, the next step is probably spelled out in the operations manual; probably something along the lines of, repeat the directive once, then assume incapacitation and take over the controls to execute the go-around.

The really bad case would be, the captain is intent on landing regardless and the FO believes that they're about to crash.  At that point, the question (really for both pilots) becomes, are you sufficiently sure of your position that fighting for the controls close to the ground is less dangerous than doing what the other pilot wants?  If we're somehow down to our last minutes of fuel &amp; the copilot wants to go around because a dog ran onto the runway, a reasonable captain would probably overrule him and land anyway.  If the captain is so intent on landing that doesn't see the aircraft on the runway that he's about to  land on top of, a reasonable copilot might push the throttles forward like his life depends on it.

If you've reached the point where "go around" "go around" "I have the aircraft, go around thrust" hasn't worked, you've left the realm of most manuals.  The implicit assumption is that an incapacitated PF isn't going to have the capacity to fight you for the controls; I doubt very many operations manuals devote much space to the nightmare case of wrestling for the controls against a maniac determined to do something awful.  Thankfully, such scenarios are almost entirely the stuff of imagination -- commercial flight is essentially the safest form of transportation ever known to mankind.  That remains true even though the one in (very literally) millions of flights where something does go horribly wrong (Germanwings crash into the Alps, etc) gets extraordinary publicity.