Limits of Semistatic Trading Strategies
Mathematical Finance
2022-04-27 v1 Probability
Abstract
We show that pointwise limits of semistatic trading strategies in discrete time are again semistatic strategies. The analysis is carried out in full generality for a two-period model, and under a probabilistic condition for multi-period, multi-stock models. Our result contrasts with a counterexample of Acciaio, Larsson and Schachermayer, and shows that their observation is due to a failure of integrability rather than instability of the semistatic form. Mathematically, our results relate to the decomposability of functions as studied in the context of Schr\"odinger bridges.
Keywords
Cite
@article{arxiv.2204.12251,
title = {Limits of Semistatic Trading Strategies},
author = {Marcel Nutz and Johannes Wiesel and Long Zhao},
journal= {arXiv preprint arXiv:2204.12251},
year = {2022}
}