On the semimartingale property of discounted asset-price processes
Abstract
A financial market model where agents trade using realistic combinations of buy-and-hold strategies is considered. Minimal assumptions are made on the discounted asset-price process - in particular, the semimartingale property is not assumed. Via a natural market viability assumption, namely, absence of arbitrages of the first kind, we establish that discounted asset-prices have to be semimartingales. In a slightly more specialized case, we extend the previous result in a weakened version of the Fundamental Theorem of Asset Pricing that involves strictly positive supermartingale deflators rather than Equivalent Martingale Measures.
Keywords
Cite
@article{arxiv.0803.1890,
title = {On the semimartingale property of discounted asset-price processes},
author = {Constantinos Kardaras and Eckhard Platen},
journal= {arXiv preprint arXiv:0803.1890},
year = {2009}
}
Comments
11 pages. The text has been thoroughly revised and there are new results. This is the 1st part of what comprised the older arxiv submission arXiv:0803.1890 "On financial markets where only buy-and-hold trading is possible" by the two authors