Hedging, arbitrage and optimality with superlinear frictions
Paolo Guasoni, Mikl\'os R\'asonyi
TL;DR
This paper analyzes how superlinear trading frictions affect superhedging, arbitrage absence, and utility maximization in continuous-time multi-asset models, revealing a duality with shadow prices and the existence of strategies despite arbitrage.
Contribution
It introduces a framework for understanding superhedging and arbitrage under general superlinear frictions, establishing duality and strategy existence results.
Findings
Superhedging prices characterized under superlinear frictions
Existence of utility-maximizing strategies even with arbitrage
Duality between trading strategies and shadow prices
Abstract
In a continuous-time model with multiple assets described by c\`{a}dl\`{a}g 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.
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Taxonomy
TopicsEconomic theories and models · Stochastic processes and financial applications · Financial Markets and Investment Strategies