Hedging under an expected loss constraint with small transaction costs

Bruno Bouchard, Ludovic Moreau, H. Mete Soner

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


We consider the problem of option hedging in a market with proportional transaction costs. Since super-replication is very costly in such markets, we replace perfect hedging with an expected loss constraint. Asymptotic analysis for small transaction costs is used to obtain a tractable model. A general expansion theory is developed using the dynamic programming approach. Explicit formulae are obtained in the special cases of exponential and power utility functions. As a corollary, we retrieve the asymptotics for the exponential utility indifference price.

Original languageEnglish (US)
Pages (from-to)508-551
Number of pages44
JournalSIAM Journal on Financial Mathematics
Issue number1
StatePublished - 2016
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Finance
  • Applied Mathematics


  • Asymptotic expansion
  • Expected loss constraint
  • Hedging
  • Transaction cost


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