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The present study applies a mathematical optimization method to solve the portfolio selection problem. This is formulated as a semi-infinite programming (SIP) problem and is solved by using a version of the stochastic outer approximation method in MATLAB. This method replaces the original problem with a sequence of optimization finite problems. The results are compared with other portfolio selection strategies such as Markowitz. Numerical experiments are performed using five years of data from eight Colombian companies that trade in the stock market. The results show that the SIP portfolio is similar to the minimum variance portfolio and that both are diversified portfolios. The maximum return portfolio is not diversified and should be discarded. Even though the naive portfolio is diversified, its performance and returns are lower than expected, but its risks are less than that of minimum variance and SIP. It is concluded that the proposed method provides satisfactory solutions when compared to the Markowitz method. [ABSTRACT FROM AUTHOR]

The binomial model presents a set of properties that make it a suitable approach in order to value the real options, throughout an easy and practical application. This is possible by the adaptation of the valuation principle for non-arbitrage, own of the options pricing theory. However, their adoption may be limited for those options that have multiple sources of uncertainty, given that their interaction should be incorporated into the valuation process. In response, financial theory has proposed valuation approaches that allow different sources of uncertainty to be represented by a consolidated estimate of volatility, such as the Marketed Asset Disclaimer (mad) approach developed by Copeland and Antikarov (2001). As an alternative, a treatment that incorporates the dynamics of each uncertainty can be given. In this context, there are different proposals that extend the Binomial model to k-dimensional or multi-dimensional context. To achieve the application, it is necessary an approximation of the k-dimensional stochastic process, as well as its correlations. This paper presents a concise review of the different methods proposed in this context, as well as their benefits, limitations and, some alternative approaches. [ABSTRACT FROM AUTHOR]

This work presents an analysis of the scaling properties of the MMLM method, used for the numerical construction of three-dimensional turbulent vector fields. Specifically, the scaling properties for the velocity field structure functions are studied. It is found that MMLM gives scaling of Kolmorogov type. If the mapping parameter, which is given by a time scale based on node separation over the computational mesh, is modified and equated to the characteristic time for eddy evolution at each spatial scale, the synthetic turbulent field presents the characteristic anomalous scaling of real turbulent fields, with very good agreement with respect to the known values. In addition, we study the intermittency and multifractal nature of the energy dissipation distribution. Results are also consistent with observations in real turbulence. The study sheds new light over the minimal dynamical requirements to obtain anomalous scaling in the inertial range. [ABSTRACT FROM AUTHOR]

This paper extends the traditional franchising valuation method based on discounted cash flows towards the framework of real options, which arises naturally as a dynamic stochastic optimization procedure where the franchisor seeks to maximize his/her utility discounted by its cost of capital subject to his/her owned wealth. This wealth includes debt costs and additional costs associated with royalties, that is to say: a lump sum and sales percentage. The latter is modelated as a variable interest rate bond through a mean-reverting process that is assumed to be stochastic and driven by a geometric Brownian motion correlated with profits. It is also shown that the capital structure irrelevance holds when there is a flat interest rate term structure. Finally, on the basis of real options sensibility, some recommendations on business strategies are stated. [ABSTRACT FROM AUTHOR]

"Multidimensional Scaling" is the name of a set of procedures with the objective of data representation in a graphical plot when some information about similarities between objects is known. The history of these procedures began with Torgeson's work in 1952 who gave the preliminary ideas. Since then many investigators have developed other works with one only aim: to obtain a euclidean representation most similar to the starting proximities between objects. In this paper we show the main purposes and some essential concepts about this thematic. [ABSTRACT FROM AUTHOR]