Finance and Stochastics

, Volume 22, Issue 2, pp 417–442 | Cite as

Perfect hedging under endogenous permanent market impacts

Article
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Abstract

We model a nonlinear price curve quoted in a market as the utility indifference curve of a representative liquidity supplier. As the utility function, we adopt a \(g\)-expectation. In contrast to the standard framework of financial engineering, a trader is no longer a price taker as any trade has a permanent market impact via an effect on the supplier’s inventory. The P&L of a trading strategy is written as a nonlinear stochastic integral. Under this market impact model, we introduce a completeness condition under which any derivative can be perfectly replicated by a dynamic trading strategy. In the special case of a Markovian setting, the corresponding pricing and hedging can be done by solving a semilinear PDE.

Keywords

Nonlinear stochastic integral \(g\)-Expectation Market impact 

Mathematics Subject Classification (2010)

60H05 91G80 

JEL Classification

G13 

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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Graduate School of Engineering ScienceOsaka UniversityOsakaJapan
  2. 2.Faculty of Mathematics and EconomicsUlm UniversityUlmGermany

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