  Motivated by the robustness of the capital distribution curves, we study the
behavior of a certain polynomial equity market model as the number of companies
goes to infinity. More precisely, we extend volatility-stabilized market models
introduced by Fernholz et al. by allowing for a common noise term such that the
models remain polynomial. As the number of companies approaches infinity, we
show that the limit of the empirical measure of the $N$-company system
converges to the unique solution of a degenerate, non-linear SPDE. The obtained
limit also has a representation as the conditional probability of the solution
to a certain McKean-Vlasov SDE. Together with its conditional, this is again a
polynomial process for which we can prove pathwise uniqueness as well as
regularity properties for the marginal densities. We also provide conditional
propagation of chaos results and numerical implementations of the particle
system as well as its limiting equations.
