Stochastic optimal control

Summary

Stochastic optimal control is optimal control of systems driven by noise, usually modelled by a stochastic differential equation. The controller chooses its action at each time from the information observed so far and minimises an expected cost. Dynamic programming leads to a second-order Hamilton–Jacobi–Bellman equation for the value function. The theory is used in engineering, in economics and in mathematical finance, for example in portfolio choice.