Properly Discounted Asset Prices Are Semimartingales

16 Pages Posted: 10 Oct 2019 Last revised: 13 Oct 2019

See all articles by Dániel Ágoston Bálint

Dániel Ágoston Bálint

ETH Zürich - Department of Mathematics

Martin Schweizer

ETH Zurich; Swiss Finance Institute

Date Written: October 3, 2019

Abstract

We study general undiscounted asset price processes, which are only assumed to be non-negative, adapted and RCLL (but not a priority semimartingales). Traders are allowed to use simple (piecewise constant) strategies. We prove that under a discounting-invariant condition of absence of arbitrage, the original prices discounted by the value of any simple strategy with positive wealth must follow semimartingales. As a side result, we establish two corresponding versions of the fundamental theorem of asset pricing that involve supermartingale discounters with some additional strict positivity property.

Keywords: semimartingales, discounting, dynamic share viability, simple strategies, noshort-sales constraints, NA1 for simple strategies, supermartingale discounter

JEL Classification: C00, G10

Suggested Citation

Bálint, Dániel Ágoston and Schweizer, Martin, Properly Discounted Asset Prices Are Semimartingales (October 3, 2019). Swiss Finance Institute Research Paper No. 19-53. Available at SSRN: https://ssrn.com/abstract=3466802 or http://dx.doi.org/10.2139/ssrn.3466802

Dániel Ágoston Bálint

ETH Zürich - Department of Mathematics ( email )

R¨amistrasse 101
Raemistr. 101
Z¨urich, 8092
Switzerland

Martin Schweizer (Contact Author)

ETH Zurich ( email )

Mathematik, HG G51.2
Raemistrasse 101
CH-8092 Zurich
Switzerland

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

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