Talks 

Abstract: Non-linear production functions are a common basis for modeling regional sales responses to marketing expenditures. A recent article of Kao et al. (2005) suggests to use such models to estimate the effectiveness of marketing strategies. In this talk the underlying approach is modified: Firstly, the model is adapted to cross-sectional observations, and secondly, a spatial component is explicitly modelled for the regional sales  %, and secondly, a hierarchical approach in the clustering of regional sales is used. The developed Cross Sectional Sales Response (CSSR) models use Stochastic Partial Derivatives (SPD) constraints. They are tested using synthetic and pharma marketing data.

Abstract: We consider strongly nonlinear long wave models for large amplitude internal waves in two-layer flows. Both rigid-lid and free-surface are set for the upper boundary. It is shown that these models suffer from the Kelvin–Helmholtz (KH) instability so that any given shear (even if arbitrarily small) between the layers makes short waves unstable. Because a jump in tangential velocity is induced when the interface is deformed, the applicability of the models to describe the dynamics of internal waves is expected to remain rather limited. To overcome this major difficulty, the models are written in terms of the horizontal velocities at certain preferred vertical levels, instead of the depth-averaged velocities. Through local stability analysis, it is shown that the new form of the models changes the dispersion relation in a way that internal solitary waves become stable to perturbations of arbitrary wavelengths, as long as their amplitudes do not exceed a certain critical value.
REFERENCES:
- Choi, W., Barros, R. & Jo, T.-C. (2009) A regularized model for strongly nonlinear internal solitary waves, J. Fluid Mech., 629:73-85.
- Barros, R. & Choi, W. (2009) Inhibiting shear instability induced by large amplitude internal solitary waves in two-layer flows with a free surface, Stud. Appl. Math., 122:325-346.
- Barros, R. & Gavrilyuk, S. L. (2007) Dispersive nonlinear waves in two-layer flows with free surface. II. Large amplitude solitary waves embedded into the continuous spectrum, Stud. Appl. Math., 119:213-251. 

Abstract: We study the optimal patent licensing under Cournot duopoly where the technology transfer takes place from an innovative firm, which is relatively cost-inefficient in the pre-innovation stage compared to the recipient firm. We determine the output levels at the Nash equilibrium and the corresponding profits of the firms. We found that the optimal licensing arrangement often involves a two part tariff, fixed fee plus a linear per unit output royalty.

Abstract: We review an extension to Merton's famous continuous time model of optimal consumption and investment, in the spirit of previous works by Pliska and Ye, to allow for a wage earner to have a random lifetime and to use a portion of the income to purchase life insurance in order to provide for his or her estate, while investing his or her savings in a financial market composed by one risk-free security and an arbitrary number of risky securities whose diffusive term is given by a multi-dimensional Brownian motion. The wage earner's problem is then to find the optimal consumption, investment, and insurance purchase decisions in order to maximize expected utility of consumption, of the size of the estate in the event of premature death, and of the size of the estate at the time of retirement. Dynamic programming methods are used to obtain explicit solutions for the case of constant relative risk aversion utility functions and some numerical results are presented with the corresponding economic interpretation. This is joint work with D. Pinheiro, A. A. Pinto and S. R. Pliska.

Abstract: As tecnologias, claramente dominantes na actualidade, que nos permitem visualizar informações representam um paradigma que denominamos de 2D. As informações são visualizadas em duas dimensões. Os exemplos desta realidade são inúmeros: monitores, televisões, vídeos, câmaras de vídeo e de fotografia, projectores, telemóveis, PDAs, cinemas, outdoors electrónicos, quiosques electrónicos, mupies, relógios, etc.
No entanto, ao longo dos últimos anos tem-se assistido a uma evolução muito rápida de um conjunto de tecnologias que denominamos genericamente de Tecnologias de Realidade Virtual (RV), que nos permitem visualizar as informações em três dimensões (3D), interagir com o ambiente e manipular conteúdos. 
Em face da rapidez da sua evolução tecnológica, diversidade de tecnologias em desenvolvimento, do aumento crescente da sua aceitação num número cada vez mais alargado de situações e da consequente baixa, significativa, de preços que se tem verificado na generalidade das mesmas tecnologias, constatamos que estamos no limiar da massificação das tecnologias de realidade virtual. Com a ocorrência deste fenómeno, estaremos em presença de uma mudança de paradigma com um profundo impacto na economia e na sociedade, a mudança do 2D para o 3D como forma, dominante, de visualizarmos e interagirmos com conteúdos.
Este impacto será maior do que a simples mudança de perspectiva que resulta da adição da noção de profundidade, pelo facto desta nova perspectiva possibilitar mudanças profundas no relacionamento entre os seres humanos e os conteúdos (informações) visualizados. Com efeito, as noções de imersividade e de interactividade ganham novas expressões e um fôlego acrescido.

Abstract: With the advent of the new Basel Capital Accord, banking organizations are invited to estimate credit risk capital requirements using an internal ratings based approach. In order to be compliant with this approach, institutions must estimate the expected loss-given-default, the fraction of the credit exposure that is lost if the borrower defaults. This study evaluates the ability of a parametric fractional response regression and a nonparametric regression tree model to forecast bank loan credit losses. The out-of-sample predictive ability of these models is evaluated at several recovery horizons after the default event. The out-of-time predictive ability is also estimated for a recovery horizon of one year. The performance of the models is benchmarked against recovery estimates given by historical averages. The results suggest that regression trees are an interesting alternative to parametric models in modeling and forecasting loss-given-default.

Abstract: We consider a  Stackelberg model with product differentiation and demand uncertainty, only for the first mover. We study the advantages of leadership and flexibility with the variation of the product differentiation  and demand uncertainty. We compute, in terms of the demand uncertainty and of the product differentiation, the probability of the second firm to have higher profit than the leading firm. We prove that, even in presence of low uncertainty, the expected value of the profit of the second firm increases to higher values than the ones of the leading firm with the increase of the product differentiation.

Abstract: This talk will address a pattern sequencing problem known in the literature as minimization of open stacks (MOSP).  This problem comes from the flat glass cutting industry, but it also has many applications in other cutting industries (wooden panels, steel tubes, paper,…) as well as in other fields such as production planning, VLSI circuit design and in classic problems from graph theory.  
Consider an industry that cuts large wooden panels in smaller panels of different sizes to meet the demands of the clients. A cutting pattern is a specification of how many subpanels of each size will be cut from a larger panel and where the cuts will be made. Usually the cutting machine can process only one pattern at a time. The different items obtained from the cutting patterns are piled in separate stacks in the work area, and they are removed to the warehouse only when all items of the same size have been cut. Due to space limitations and danger of damages on the stacked items, it is advantageous to find a sequence for processing the cutting patterns that minimizes the number of different items that are being cut and therefore the number of open stacks.
The resulting situation can be explained by exhibiting a set of intervals that match the duration of each stack.  A solution can be modelled by an interval graph where each vertex corresponds to the interval of time that each stack is open and edges exist between vertices if the corresponding stacks are simultaneously open during a certain period of time. Using an integer programming model, an optimal solution can be found as an interval graph obtained by densifying the original MOSP graph.

Abstract: We calculate probability distributions F_{S&P100,+} and F_{S&P100,-} of the normalized positive and negative Standard&Poor's 100 (S&P100) index daily returns r(t). Furthermore, we  define the alpha re-scaled S&P100 daily index positive returns  r(t)^alpha and negative returns (-r(t))^alpha that we call, after normalization, the alpha positive fluctuations and alpha negative  fluctuations. We use the Kolmogorov-Smirnov statistical test, as a method, to find the values of  alpha that optimize the data collapse of the histogram of the  alpha  fluctuations  with the Bramwell-Holdsworth-Pinton (BHP) probability density function. The optimal parameters that we found are alpha^{+}= 0.51  and alpha^{-}= 0.48. Since the BHP probability density function appears in several other dissimilar phenomena, our result reveals an universal feature of the stock exchange markets.