Chair: Susana Nicola, ISEP - Instituto Superior de Engenharia do Porto; IPP – Instituto Politécnico do Porto, Portugal
Stopping times for fractional Brownian motion
Pavel Gusyatnikov (email@example.com), Alexander Kulikov (firstname.lastname@example.org)
The basic models used in financial mathematics are based on Markov processes and semimartingales. Nevertheless not all prices correspond to such processes. Fractional Brownian motion is an example of such process used in practice. It is a stochastic process with parameter H, first described by Mandelbrot and Van Ness in 1968. Cheredito and Guasoni have shown that in arbitrage theory with transactional costs fractional Brownian motion does not have an arbitrage strategy. In this paper we consider an optimal stopping problem i.e. a choice of optimal selling time t between 0 and T for an asset, which price is described by a fractional Brownian motion. In case of classical Brownian motion it can be shown that a decision making rule for an investor can be represented as “Buy and Hold”. This means that an investor should sell assets either at moment of time t = 0 or at moment of time t=T depending on drift parameter. In this paper a discretization of fractional Brownian motion and a set of stopping times for this discritezation is considered. The first natural stopping time is the first moment when the drift of the next increment is negative. It will be shown that this set of stopping times gives non trivial results. Numerical results were obtained and an example of non optimality of this stopping time is also proposed. In this paper a more complex stopping time for fractional Brownian motion is also considered. It is shown that it gives better results and is not very complex for modeling as well.
Keywords: fractional Brownian motion, drift, optimal stopping problem
Explanation of the classification by the approach of rough sets on the example of the classification of municipalities in the territory of Northern Quebec
Kazimierz Zaras (Kazimierz.Zaras@uqat.ca), Jean-Charles Marin (email@example.com), Bryan Boudreau-Trudel (firstname.lastname@example.org)
The object of our research was classification of the 52 municipalities in the territory of Northern Quebec made from 32 socio-economic indicators measures in six dimensions: demographic, sociological, micro-economic, employment, income and professions using the multicriteria method of weighted ranks. Based on this classification the municipalities were delimited by quartiles relative to the average ranking to one of four categories: [A] – the best in the region in terms of the criteria considered; [B] – those that need support in order to acquire category A status; [C] – those that need support in order to acquire category B status; [D] – those ranked lowest in the region and needing special support with regard to the criterion or criteria considered. The originality of our approach is the fact that from the classification of municipalities using a rough set method known as the Dominance-based rough set approach DRSA, we made the extraction of decision rules such as "if ... then" explaining why the municipality was classified in such and such a category, what criteria were relevant in this classification? What are the critical values of the criteria for discriminating each class? These decision rules thus focus on the social and economic needs of municipalities with respect to improving their performance and classification. By targeting these needs, DRSA will help administrators of the Northern Quebec development plan to prioritize actions or to evaluate, for example the social and economic impact of a project in a municipality.
Keywords: Classification, Rough Sets, DRSA
A New and Innovative Approach to Assess and Quantify the Value for the Customer
Susana Nicola (email@example.com), Eduarda Pinto Ferreira (firstname.lastname@example.org), João José Pinto Ferreira (email@example.com)
This paper builds on the application of the Conceptual Model Decomposing Value for the Customer framework and a quantitative model used to access the adequacy of both enterprise offering to the customer needs and of its supporting assets, based on the different dimension on value creation analysis. This innovative approach results from the research developed in previous three case studies, and on the experience acquired in the data collection process, analysis and final discussion with the companies. In this context, we proposed ``three steps approach'' to decomposing and assessing the value for the customer, enabling a systematic application of the process for future projects. We hope that our research on Value for the Customer as well as concerning the development of the CMDVC will contribute not only to extend and improve the existence of the knowledge foundations. We further hope to produce significant value to enterprises if they want to assess the value proposition of their offer and, moreover, if they want to understand the adequacy of their enterprise assets to support the desired value proposition.
Keywords: Value for the Customer, Value creation analysis, Fuzzy AHP