On the Stickiness Property

TL;DR

This paper explores the concept of stickiness in stochastic processes, providing examples of non-semimartingale processes that are sticky, and discusses implications for market arbitrage with transaction costs.

Contribution

It extends the notion of stickiness by presenting non-semimartingale examples, deepening understanding of its role in financial market models.

Findings

Identified non-semimartingale processes that are sticky

Demonstrated stickiness implies no arbitrage in markets with transaction costs

Expanded the class of processes known to be sticky

Abstract

In [2] the notion of stickiness for stochastic processes was introduced. It was also shown that stickiness implies absense of arbitrage in a market with proportional transaction costs. In this paper, we investigate the notion of stickiness further. In particular, we give examples of processes that are not semimartingales but are sticky.