Preface These are the extended version of the Cattedra Galileiana I gave in April 2003 in Scuola Normale, Pisa. I am grateful to the Society of Amici della Scuola Normale for the funding and to Professors Maurizio Pratelli, Marzia De Donno and Paulo Guasoni for organizing these lectures and their hospitality. In these notes, I give a very quick introduction to stochastic optimal control and the...

2 Stochastic optimal control (discrete time) 2 2.1 The Linear-quadratic-Gaussian (LQG) case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Message passing in LQG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.3 Special case: kinematic control . . . . . . . . . . . . . . . . . . . . . . . . . ...

In this paper we describe a model of the immunologic response of the human immunodeficiency virus (HIV) in individuals. We illustrate how optimal control methodology can produce a drug dosing strategy and how this treatment strategy possesses features of structured treatment interruptions (STI). We then perform a sensitivity analysis of the model, illustrating use of both classical sensitivity ...

We obtain the optimal harvesting plan to maximize the expected discounted number of individuals harvested over an infinite future horizon, under the most common (»erhulst-Pearl) logistic model for a stochastically fluctuating population. We also solve the problem for the standard variants of the model where there are constraints on the admissible harvesting rates. We use stochastic calculus to ...