Research projects

Project CEMAPRE internal

TitleOptimization, differential equations, and applications
ParticipantsManuel Guerra (Principal Investigator), João Janela, Carlos Oliveira, Carlos Miguel S Oliveira, Andrey Sarychev, Rúben A Sousa
SummaryThere 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 developped
theory of deterministic systems.
In this project we will study certain types of infinitesimal generators, relating their properties
with usefull 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