Optimal pricing, use and exploration of uncertain natural resources

Patrick S. Hagan, Diana E. Woodward, Russel E. Caflisch, Joseph B. Keller

Research output: Contribution to journalArticlepeer-review


We consider Arrow's model for an economy engaged in consuming a randomly distributed natural resource, and in exploring previously unexplored land to find more of the resource. After modifying the model so that each discovery reveals a random amount of the resource, we use dynamic programming techniques to derive the equations governing optimal rates of exploration, consumption, and pricing of the resource. We analyse these equations asymptotically when the typical amount discovered is small compared with the total amount of the resource, and approximately when the amount is medium or large. In both cases we obtain formulas for the optimal exploration, consumption, and pricing policies. We demonstrate the accuracy of these analytical results by comparing them with numerically-determined exact solutions, and discuss economic implications of these results.

Original languageEnglish (US)
Pages (from-to)87-108
Number of pages22
JournalApplied Mathematical Finance
Issue number1
StatePublished - Sep 1994


  • dynamic programming
  • optimal pricing

ASJC Scopus subject areas

  • Finance
  • Applied Mathematics


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