  A stock market is called diverse if no stock can dominate the market in terms
of relative capitalization. On one hand, this natural property leads to
arbitrage in diffusion models under mild assumptions. On the other hand, it is
also easy to construct diffusion models which are both diverse and free of
arbitrage. Can one tell whether an observed diverse market admits arbitrage?
  In the present paper we argue that this may well be impossible by proving
that the known examples of diverse markets in the literature (which do admit
arbitrage) can be approximated uniformly (on the logarithmic scale) by models
which are both diverse and arbitrage-free.
