Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fundamental theorems of asset pricing for piecewise semimartingales of
  stochastic dimension   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.

25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
2
The categories of this paper are: math