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.
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.
Abstract
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.
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