Continuous-time security pricing. A utility gradient approach

Darrell Duffie*, Costis Skiadas

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

110 Scopus citations


We consider a (not necessarily complete) continuous-time security market with semimartingale prices and general information filtration. In such a setting, we show that the first-order conditions for optimality of an agent maximizing a 'smooth' (but not necessarily additive) utility can be formulated as the martingale property of prices, after normalization by a 'state-price' process. The latter is given explicitly in terms of the agent's utility gradient, which is in turn computed in closed form for a wide class of dynamic utilities, including stochastic differential utility, habit-forming utilities, and extensions.

Original languageEnglish (US)
Pages (from-to)107-131
Number of pages25
JournalJournal of Mathematical Economics
Issue number2
StatePublished - Mar 1994


  • Asset pricing
  • Continuous time
  • Dynamic utility
  • Habit formation
  • Martingale method
  • State prices
  • Stochastic differential utility

ASJC Scopus subject areas

  • Economics and Econometrics
  • Applied Mathematics


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