In addition towhat has already been said, you should consider whether all abbreviations are necessary. Some are part of jargon but sometimes you see something abbreviated only to be used, say, twice. In such a case it is unnecessary. My advice is to be relatively restrictive with new abbreviations and ones that are not used very frequently.
I personally think there is a tendency to over-use abbreviations and making wise decisions of when to use them and when not to use them should be part of all scientific writing. In the days when papers were printed on paper there may have been an incentive to make the text shorter but with digital publications, this is no longer really the case.
Whether you should re-introduce some abbreviations in each chapter, I think it is a matter of style and taste. The purpose of reiterating the explanation would be if you think the use is rare so that the reader would forget about them between occurrences. Then it may be useful to drop them altogether.
Variables are slightly different. You should only need to provide an explanation once. That in addition with a list of variables should be sufficient.
As a comment, in your example you abbreviate Monte Carlo simulation as MC and in the second sentence you essentially say "Monte Carlo is a stochastic process" (it is a place). You should use MCS to make the abbreviation full and not subject to misinterpretation.