I agree that there may be some aggregation problem. This paper says :"Cumulative Prospect Theory (CPT) has been used as a possible explanation of aggregate pricing anomalies like the equity premium puzzle. This paper shows that, unlike in expected-utility models, a complete market is not sufficient to guarantee that the market portfolio is efficient, and that the standard representative-agent analysis is valid. The separation or mutual fund theorems hold only under very restrictive conditions for CPT investors. Without them, aggregation breaks down, and assets are not necessarily priced as if there were one investor who behaved according to CPT. Under more limited conditions, the market portfolio can be efficient in a complete market with equally probable states. But in this case, individual CPT investors behave in the aggregate like a standard expected utility investor. Similarly, when faced with elliptically distributed assets, the CAPM holds for any combination of CPT investors and expected utility maximizers."(ref here http://cfr.ivo-welch.info/2014/ingersoll-cpt-2014.pdf
)But in fact the fact that the "representative agent" does not hold is maybe a good point (I hate the idea that you could model the collective behaviour of an ensemble of irrational guys by a single rational fictive character). Portfolio aggregation are also more difficult due to the nonlinear nature of the stuff but I remember that you have nothing against nonlinearity For me there is just a funny stuff, is that the authors still consider the maximization of the expectation as if the investor "rationnally" maximize their "irrational utility". Very funny In my opinion, people (not professional investor) TRY TO MAXIMIZE (and not fully maximize) their FUTURE EXPECTATION CONDITIONAL TO THEIR PRESENT BELIEF (which is not the same that the mathematical expectation with all the available information). But CPT is a good start.