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Perfect hedging under endogenous permanent market impacts

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  • Masaaki Fukasawa
  • Mitja Stadje

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 more price taker as any trade has a permanent market impact via an effect to 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 semi-linear PDE.

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  • Masaaki Fukasawa & Mitja Stadje, 2017. "Perfect hedging under endogenous permanent market impacts," Papers 1702.01385, arXiv.org.
  • Handle: RePEc:arx:papers:1702.01385
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