Control with partial observations and an explicit solution of Mortensen's equation

Václav E. Benes, Ioannis Karatzas, Daniel Ocone, Hui Wang

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


We formulate a stochastic control problem with a general information structure, and show that an optimal law exists and is characterized as the unique solution of a recursive stochastic equation. For a special information structure of the "signal-plus-noise" type and with quadratic cost-functions, this recursive equation is solved for the value function of the control problem. This value function is then shown to satisfy the Mortensen equation of Dynamic Programming in function-space.

Original languageEnglish (US)
Pages (from-to)217-239
Number of pages23
JournalApplied Mathematics and Optimization
Issue number3
StatePublished - May 2004

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Applied Mathematics


  • Filtering
  • Komlós theorem
  • Mortensen equation
  • Partial observations
  • Recursive stochastic equations
  • Stochastic control


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