Fundamental theorems of asset pricing for piecewise semimartingales of stochastic dimension
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Date
2011-12-22Type
- Working Paper
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Abstract
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. Show more
Publication status
publishedExternal links
Journal / series
arXivPages / Article No.
Publisher
Cornell UniversitySubject
Semimartingale; Martingale; Stochastic integration; Fundamental theorem of asset pricing; Stochastic dimensionOrganisational unit
03658 - Schweizer, Martin / Schweizer, Martin
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Is previous version of: https://doi.org/10.3929/ethz-b-000088121
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