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When Limits of Semistatic Trading Strategies Remain Semistatic

Article arXiv papers · Author: Marcel Nutz et al.
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Summary

The document studies whether pointwise limits of semistatic trading strategies remain within the same class. It establishes this property in discrete time for a general two-period model, and extends the result to models with multiple periods and stocks when a probabilistic condition holds. This is a mathematical result about the structure of strategies under limits, rather than a practical signal or trade-selection method.

The authors contrast their findings with a previously reported counterexample, attributing that case to a failure of integrability rather than instability of semistatic strategies themselves. They also connect the analysis to decomposability of functions in the study of Schrödinger bridges. The stated multi-period result depends on an additional probabilistic condition, and the short description does not specify that condition or provide examples, so applying the result requires consulting the full mathematical treatment.

Key ideas

  • In discrete time, pointwise limits of semistatic strategies remain semistatic in a general two-period model.
  • The multi-period, multi-stock result requires a probabilistic condition.
  • The authors explain a prior counterexample through failure of integrability.
  • The analysis connects semistatic strategy limits with mathematical decomposability and Schrödinger bridges.

Tags

StatisticsRisk managementPortfolio construction
Full text
# Limits of Semistatic Trading Strategies


# Limits of Semistatic Trading Strategies









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 Schrödinger bridges.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.