TITLE

Fundamental theorems of asset pricing for piecewise semimartingales of stochastic dimension

AUTHOR(S)
Strong, Winslow
PUB. DATE
July 2014
SOURCE
Finance & Stochastics;Jul2014, Vol. 18 Issue 3, p487
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
This paper has two purposes. The 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. The second purpose 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.
ACCESSION #
97072645

 

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