Backward SDEs for control with partial information

Andrew Papanicolaou

Research output: Contribution to journalArticlepeer-review


This paper considers a non-Markov control problem arising in a financial market where asset returns depend on hidden factors. The problem is non-Markov because nonlinear filtering is required to make inference on these factors, and hence the associated dynamic program effectively takes the filtering distribution as one of its state variables. This is of significant difficulty because the filtering distribution is a stochastic probability measure of infinite dimension, and therefore the dynamic program has a state that cannot be differentiated in the traditional sense. This lack of differentiability means that the problem cannot be solved using a Hamilton–Jacobi–Bellman equation. This paper will show how the problem can be analyzed and solved using backward stochastic differential equations, with a key tool being the problem's dual formulation.

Original languageEnglish (US)
Pages (from-to)208-248
Number of pages41
JournalMathematical Finance
Issue number1
StatePublished - Jan 2019


  • backward stochastic differential equations
  • non-Markov control
  • partial information
  • portfolio optimization

ASJC Scopus subject areas

  • Accounting
  • Finance
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Applied Mathematics


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