Dynamic trading under integer constraints



Gerhold, Stefan and Kruhner, Paul
(2018) Dynamic trading under integer constraints. FINANCE AND STOCHASTICS, 22 (4). pp. 919-957.

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Abstract

In this paper we investigate discrete time trading under integer constraints, that is, we assume that the offered goods or shares are traded in integer quantities instead of the usual real quantity assumption. For finite probability spaces and rational asset prices this has little effect on the core of the theory of no-arbitrage pricing. For price processes not restricted to the rational numbers, a novel theory of integer arbitrage free pricing and hedging emerges. We establish an FTAP, involving a set of absolutely continuous martingale measures satisfying an additional property. The set of prices of a contingent claim is no longer an interval, but is either empty or dense in an interval. We also discuss superhedging with integral portfolios.

Item Type: Article
Uncontrolled Keywords: Arbitrage, Hedging, Integer constraints
Depositing User: Symplectic Admin
Date Deposited: 03 Dec 2018 16:19
Last Modified: 19 Jan 2023 01:10
DOI: 10.1007/s00780-018-0369-3
Open Access URL: https://link.springer.com/content/pdf/10.1007/s007...
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3029440