Applied Mathematics and Optimization

, Volume 22, Issue 1, pp 229-240

First online:

The optimal control of diffusions

  • Robert J. ElliottAffiliated withDepartment of Statistics and Applied Probability, University of Alberta

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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.