characterized by removing the time subscripts from its dynamic equation. Continuous time If the model is in continuous time, the controller knows the state of the system at each instant of time. The objective is to maximize either an integral of, for example, a concave function of a state variable over a horizon from time zero (the present) to a terminal time T, or a concave function of a state variable at some future date T. As time evolves, new observations are continuously made and the control variables are continuously adjusted in optimal fashion. Stochastic model predictive control In the literature, there are two types of MPCs for stochastic systems; Robust model predictive control and Stochastic Model Predictive Control (SMPC). Robust model predictive control is a more conservative method which considers the worst scenario in the optimization procedure. However, this method, similar to other robust controls, deteriorates the overall controller's performance and also is applicable only for systems with bounded uncertainties. The alternative method, SMPC, considers soft constraints which limit the risk of violation by a probabilistic inequality. In finance In a continuous time approach in a finance context, the state variable in the stochastic differential equation is usually wealth or net worth, and the controls are the shares placed at each time in the various assets. Given the asset allocation chosen at any time, the determinants of the change in wealth are usually the stochastic returns to assets and the interest rate on the risk-free asset. The field of stochastic control has developed greatly since the 1970s, particularly in its applications to finance. Robert Merton used stochastic control to study optimal portfolios of safe and risky assets. His work and that of Black–Scholes changed the nature of the finance literature. Influential mathematical textbook treatments were by Fleming and Rishel, and by Fleming and Soner. These techniques were applied by Stein to the financial crisis of 2007–08. The maximization, say of the expected logarithm of net worth at a terminal date T, is subject to stochastic processes on the components of wealth. In this case, in continuous time Itô's equation is the main tool of analysis. In the case where the maximization is an integral of a concave function of utility over an horizon (0,T), dynamic programming is used. There is no certainty equivalence as in the older literature, because the coefficients of the control variables—that is, the returns received