  The purpose of this paper is two-fold. First is to extend the notions of an
n-dimensional semimartingale and its stochastic integral to a piecewise
semimartingale of stochastic dimension. The properties of the former carry over
largely intact to the latter, avoiding some of the pitfalls of
infinite-dimensional stochastic integration. Second is to extend two
fundamental theorems of asset pricing (FTAPs): the equivalence of no free lunch
with vanishing risk to the existence of an equivalent sigma-martingale measure
for the price process, and the equivalence of no arbitrage of the first kind to
the existence of an equivalent local martingale deflator for the set of
nonnegative wealth processes.
