  This paper studies an equity market of stochastic dimension, where the number
of assets fluctuates over time. In such a market, we develop the fundamental
theorem of asset pricing, which provides the equivalence of the following
statements: (i) there exists a supermartingale num\'eraire portfolio; (ii) each
dissected market, which is of a fixed dimension between dimensional jumps, has
locally finite growth; (iii) there is no arbitrage of the first kind; (iv)
there exists a local martingale deflator; (v) the market is viable. We also
present the optional decomposition theorem, which characterizes a given
nonnegative process as the wealth process of some investment-consumption
strategy. Furthermore, similar results still hold in an open market embedded in
the entire market of stochastic dimension, where investors can only invest in a
fixed number of large capitalization stocks. These results are developed in an
equity market model where the price process is given by a piecewise continuous
semimartingale of stochastic dimension. Without the continuity assumption on
the price process, we present similar results but without explicit
characterization of the num\'eraire portfolio.
