Applied Mathematics and Optimization

, Volume 22, Issue 1, pp 229–240

The optimal control of diffusions

  • Robert J. Elliott

DOI: 10.1007/BF01447329

Cite this article as:
Elliott, R.J. Appl Math Optim (1990) 22: 229. doi:10.1007/BF01447329


Using a differentiation result of Blagovescenskii and Freidlin calculations of Bensoussan are simplified and the adjoint process identified in a stochastic control problem in which the control enters both the drift and diffusion coefficients. A martingale representation result of Elliott and Kohlmann is then used to obtain the integrand in a stochastic integral, and explicit forward and backward equations satisfied by the adjoint process are derived.

Copyright information

© Springer-Verlag New York Inc. 1990

Authors and Affiliations

  • Robert J. Elliott
    • 1
  1. 1.Department of Statistics and Applied ProbabilityUniversity of AlbertaEdmontonCanada