English

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}
}