Project CEMAPRE internal
| Title | Optimization, functional analysis, and applications |
| Participants | Nuno Brites, Manuel Guerra (Principal Investigator), João Guerra, Alexandra Moura, Phuong Nguyen, Carlos Oliveira, Andrey Sarychev |
| Summary | There is a one-to-one correspondence between strongly continuous Markov processes and evolution equations driven by closed dissipative operators. The study of such operators is a classical and powerful approach to the study of the associated stochastic processes. Also, the study of controlled versions of evolution equations is interesting in itself, and provides an alternative to more classical approaches to the control of stochastic processes. One advantage of this approach is that it allows for the use of tools from the well developed theory of deterministic systems. In this project we will study certain types of infinitesimal generators, relating their properties with useful properties of the corresponding stochastic processes. We will also study general control-theoretic properties of evolution equations and their relation to control of associated stochastic processes. Applications in the fields of optimal stochastic control, optimal stopping, and related problems in mathematical finance and economics will also be considered. The project will seek to obtain both analytic and numerical results. |