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Superlinear Frictions 
Hedging, Arbitrage, and Optimality 
with Superlinear Frictions 
Paolo Guasoni1;2 Miklós Rásonyi3;4 ...
Superlinear Frictions 
Market Depth 
 Depth: 
the size of an order flow innovation required to change prices a given 
amou...
Superlinear Frictions 
Theory 
 Usual questions: arbitrage, hedging, optimality. 
 Discrete time: 
Astic and Touzi (2007),...
Superlinear Frictions 
Results in a Nutshell 
 Risky asset: cadlag process St . 
 Number of shares t = 
R t 
0 sds. Effect...
Hedging, Arbitrage, and Optimality with Superlinear Frictions
Hedging, Arbitrage, and Optimality with Superlinear Frictions
Hedging, Arbitrage, and Optimality with Superlinear Frictions
Hedging, Arbitrage, and Optimality with Superlinear Frictions
Hedging, Arbitrage, and Optimality with Superlinear Frictions
Hedging, Arbitrage, and Optimality with Superlinear Frictions
Hedging, Arbitrage, and Optimality with Superlinear Frictions
Hedging, Arbitrage, and Optimality with Superlinear Frictions
Hedging, Arbitrage, and Optimality with Superlinear Frictions
Hedging, Arbitrage, and Optimality with Superlinear Frictions
Hedging, Arbitrage, and Optimality with Superlinear Frictions
Hedging, Arbitrage, and Optimality with Superlinear Frictions
Hedging, Arbitrage, and Optimality with Superlinear Frictions
Hedging, Arbitrage, and Optimality with Superlinear Frictions
Hedging, Arbitrage, and Optimality with Superlinear Frictions
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Hedging, Arbitrage, and Optimality with Superlinear Frictions

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In a continuous-time model with multiple assets described by cadlag 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. With such frictions, dual elements correspond to a pair of a shadow execution price combined with an equivalent martingale measure. For utility functions defined on the real line, optimal strategies exist even if arbitrage is present, because it is not scalable at will.

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Hedging, Arbitrage, and Optimality with Superlinear Frictions

  1. 1. Superlinear Frictions Hedging, Arbitrage, and Optimality with Superlinear Frictions Paolo Guasoni1;2 Miklós Rásonyi3;4 Boston University1 Dublin City University2 MTA Alfréd Rényi Institute of Mathematics, Budapest3 University of Edinburgh4 Analyse stochastique pour la modélisation des risques CIRM, September 10th, 2014
  2. 2. Superlinear Frictions Market Depth Depth: the size of an order flow innovation required to change prices a given amount (Kyle, 1985) Documented empirically: Amihud (2002), Admati and Pfleiderer (1988), Cho (2007) In Illiquid Portfolio Choice: Rogers and Singh (2010), Garleanu and Pedersen (2013) In Optimal Liquidation: Almgren and Chriss, (2001), Bertsimas and Lo (1998), Schied and Schöneborn (2009) Unlike frictionless markets, trading affects prices. Unlike transaction costs, prices depend on direction and speed.
  3. 3. Superlinear Frictions Theory Usual questions: arbitrage, hedging, optimality. Discrete time: Astic and Touzi (2007), Pennanen and Penner (2010), Dolinsky and Soner (2013) Continuous Time: Cetin, Soner, and Touzi (2010), Cetin and Rogers (2007). Which trading strategies? Attainable payoffs?
  4. 4. Superlinear Frictions Results in a Nutshell Risky asset: cadlag process St . Number of shares t = R t 0 sds. Effect of friction G on wealth Xt : dXt = tdSt

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