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Superlinear Trading Frictions, Superhedging, and Arbitrage

Article arXiv papers · Author: Paolo Guasoni et al.
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Summary

This paper studies superhedging prices, arbitrage, and utility-maximizing strategies in a continuous-time market with multiple assets whose prices follow càdlàg processes. Its central feature is a class of trading frictions that become increasingly unfavorable as trading intensity rises. The analysis links these costs to a dual representation involving feasible strategies, shadow execution prices, and a martingale measure.

A notable implication is that utility-maximizing strategies can exist even when arbitrage opportunities are present: the frictions prevent those opportunities from being scaled without limit. This challenges the assumption that the presence of any arbitrage necessarily rules out sensible utility optimization. The abstract states theoretical characterizations, but gives no empirical application, specific market calibration, or quantitative comparison. Practical conclusions therefore depend on how well a particular market’s execution costs fit the model’s assumptions.

Key ideas

  • The paper characterizes superhedging prices and arbitrage in a multi-asset continuous-time market.
  • Trading costs worsen as trading intensity increases.
  • The framework links feasible strategies to shadow execution prices and a martingale measure.
  • Utility-maximizing strategies may exist even when arbitrage is present.
  • The stated results are theoretical and do not include an empirical market calibration.

Tags

ArbitrageExecutionMarket microstructureRisk management
Full text
# Hedging, arbitrage and optimality with superlinear frictions


# Hedging, arbitrage and optimality with superlinear frictions









In a continuous-time model with multiple assets described by càdlàg processes, this paper characterizes superhedging prices, absence of arbitrage, and utility maximizing strategies, under general frictions that make execution prices arbitrarily unfavorable for high trading intensity. Such frictions induce a duality between feasible trading strategies and shadow execution prices with a martingale measure. Utility maximizing strategies exist even if arbitrage is present, because it is not scalable at will.

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.