Thanks for the clarification. I did not know that reference, and it seems we're much more in alignment than I thought.
I still hold that the target moves discontinuously, though not universally so. Death is the strongest argument here. A set of preferences exists, and then it doesn't. Some deaths are expected. Some are slow. Some are unexpected. Some are abrupt. Death is a binary off-switch for all preferences the deceased individual may have had. Without this collection of preferences, equilibrium abruptly jumps to some other value. Of course, in a system as large as the market, these death-jumps are going to be so small as to be effectively immeasurable.
Note: expectation of death here means at a specific time. All death is expected on a long enough time scale.
> To a good approximation, markets moves continuously
I agree here. My discussion of discontinuity, though, is that of movement of whatever ideal equilibrium the market is moving toward (but does not achieve). The equilibrium is the target toward which a market moves. This equilibrium is incalculable or at least not calculable in less time than it would take to reach. The target may move discontinuously (though I would argue the discontinuities are small for the most part), and the process moving toward the target may be continuous, both at the same time.
Ninja edit: An equilibrium in this discussion is more akin to a platonic ideal than anything concrete. The market is the system which can be observed. The equilibrium is an abstract and incalculable target.