turkmath.org

Starting with the moon-landing problem, the mathematical theory of  optimal control has been fully developed and found numerous applications not only in engineering but also in many subfields of social sciences. In particular, in economics and quantitative finance, stochastic optimal control has become a  central modeling tool, and is the starting point for many modern learning algorithms.  The unifying paradigm is decisions under uncertainty and one imagines that a rational decision maker is guided by an appropriate control problem.  In this talk, after describing the structure of the general problem, I will outline the powerful solution technique based on dynamic programming.  Several applications such as the Kalman filter used in automated machines,  Merton’s problem for optimal investment decisions and the Ellsberg experiment for uncertainty will also be discussed.  I will conclude with the new developments and the questions.