Pricing and hedging in incomplete markets

Peter Carr, Helyette Geman, Dilip B. Madan

Research output: Contribution to journalArticlepeer-review


We present a new approach for positioning, pricing, and hedging in incomplete markets that bridges standard arbitrage pricing and expected utility maximization. Our approach for determining whether an investor should undertake a particular position involves specifying a set of probability measures and associated floors which expected payoffs must exceed in order for the investor to consider the hedged and financed investment to be acceptable. By assuming that the liquid assets are priced so that each portfolio of assets has negative expected return under at least one measure, we derive a counterpart to the first fundamental theorem of asset pricing. We also derive a counterpart to the second fundamental theorem, which leads to unique derivative security pricing and hedging even though markets are incomplete. For products that are not spanned by the liquid assets of the economy, we show how our methodology provides more realistic bid-ask spreads.

Original languageEnglish (US)
Pages (from-to)131-167
Number of pages37
JournalJournal of Financial Economics
Issue number1
StatePublished - Oct 2001


  • Complete markets
  • G12
  • G13
  • Option pricing
  • Risk management
  • State price density
  • Unique Martingale measure

ASJC Scopus subject areas

  • Accounting
  • Finance
  • Economics and Econometrics
  • Strategy and Management


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