Main Speakers and minicoursesTimetable
Abstract: During the course two practical problems are introduced and modelled. The mathematical modelling discussion of these problems is used to exemplify several issues occurring during the resolution of practical problems, such as: the importance of mathematical modelling and theoretical research in solving real problems; discrepancies between solving theoretical and real problems; importance of interdisciplinary.
Abstract: Many industrial processes involves several physical phenomena, usually coupled. The course deals with some examples arising from the metallurgical and the power generation industries. The first part concerns mathematical modelling and numerical simulation of induction furnaces. We introduce the models for the electromagnetic, thermodynamic and fluid dynamic phenomena, analyse the couplings among them, and propose numerical methods for computing their solution. The second part, we will consider mathematical modelling of pulverized coal boilers. This process involves two-phase reacting flows. We consider coupled models for the gas and the condensed phases and propose numerical methods for their solution.
Abstract: Flow control is one of the most challenging and relevant topics connecting the theory of Partial Differential Equations (PDE) and Control Theory. On one hand the number of possible applications is huge including optimal shape design in aeronautics. On the other hand, from a purely mathematical point of view it involves sophisticated models such as Navier-Stokes and Euler equations, hyperbolic systems of conservations laws, that constitute, certainly, one of the main challenges of the theory of PDE. Indeed, some of the main issues concerning existence, uniqueness and regularity of solutions are still open in this field. Moreover, Control Theory also faces some added difficulties when addressing these issues since the possible presence of singularities on solutions makes often classical approaches fail.
In this minicourse we present recent joint work in collaboration with Carlos Castro and Francisco Palacios in which we propose a new alternate direction method that allows not only dealing with shocks but also taking advantage of their presence to make the optimization processes to converge much master.
Abstract: These lectures will cover the three basic quantitative methods of portfolio management beginning with the mean-variance approach introduced by Harry Markowitz. Being a trade-off between risk and expected return, this involves quadratic programming. Second is the expected utility maximization approach that was introduced in a discrete time context by Samuelson and solved with dynamic programming. Merton extended this to continuous time and, using stochastic control theory, showed how to solve this with PDE’s. Third, the speaker introduced the risk neutral approach for portfolio management. Here the problem of maximizing the expected utility of terminal wealth is solved via martingale theory and convex optimization theory. Some examples will be given of how these approaches might have been applied to some recent financial data. If time permits attention will be given to some extensions such as risk sensitive portfolio management and the inclusion of features like consumption, income, and the opportunity to buy life insurance.
Edificio das Matematicas da FCUP
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