You can just carry any non-100% gain/loss "swimlane" as a game still-in-progress. Eventually on larger time scale, puchasing power adjusted or not, a swimlane of an investment will certainly hit one of those outcomes.
The outcome is a function of time but a large number of swimlanes guarantees that you can sample any time and observe the same distribution of settled outcomes. You can reasonably assume that the probability of transition from unsettled to settled state at any time is constant. You could model it as markov process. In fact there are many economic agent models doing something like this (OLG models where generations of economic agents overlap in time as child/worker/retiree). Even though these models make sense only on generational scale, with enough agents you can see the micro-structure being consistent in smaller time scales by "ticking" or sampling at smaller time steps the markov process.
The spending power issue could be ignored as "without loss of generality" in most cases or the thesis could be restated in terms of something that preserves purchasing power as part of the coin toss game.
Investment returns mean-revert only if allowed to by policy. Policy can override economic forces for very long generational time scales, thus making it still relevant for individuals.
And I personally don't agree with (or don't understand) these models being used for micro-structure analysis, but I think macro-level interpretations such as wealth distribution may be valid.