The optimal control of diffusions
- 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.