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Perfect hedging under endogenous permanent market impacts

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  • Masaaki Fukasawa

    () (Osaka University)

  • Mitja Stadje

    (Ulm University)

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 $g$ -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.

Suggested Citation

  • Masaaki Fukasawa & Mitja Stadje, 2018. "Perfect hedging under endogenous permanent market impacts," Finance and Stochastics, Springer, vol. 22(2), pages 417-442, April.
  • Handle: RePEc:spr:finsto:v:22:y:2018:i:2:d:10.1007_s00780-017-0352-4
    DOI: 10.1007/s00780-017-0352-4
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    References listed on IDEAS

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    Cited by:

    1. Thai Nguyen & Mitja Stadje, 2020. "Forward BSDEs and backward SPDEs for utility maximization under endogenous pricing," Papers 2005.04312, arXiv.org.

    More about this item

    Keywords

    Nonlinear stochastic integral; g $g$ -Expectation; Market impact;

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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