Salvador Cruz Rambaud

A note on the reasonableness of PERT hypotheses

In this paper the expression for the mean in the PERT method is considered. This mean involves a parameter k, that sometimes has been set to 4. Insisting on the similarity between the beta and the normal distributions, certain hypotheses are proposed that lead to k necessarily being exactly 4. More specifically, by using the moments of the second and fourth orders, it is shown that the usual beta distribution in the PERT method is mesokurtic (@c=3) and of constant variance (@s^2=136).

The two-sided power distribution for the treatment of the uncertainty in PERT

The aim of this paper is to include the Two-Sided Power (TSP) distribution in the PERT methodology making use of the advantages that this four-parameter distribution offers. In order to be completely determined, a distribution of this type needs, the same as the beta distribution, a new datum apart from the three usual values a (pessimistic), m (most likely) and b (optimistic). To solve this question, when using the beta distribution in the PERT context, we are looking for the maximum similarity with the normal and so it is required that the distribution has the same variance as the normal or its same kurtosis, giving rise to the constant variance and mesokurtic families, respectively. Nevertheless, while this approach can be only applied to the beta distribution for some values in the range of the standardized mode, in the case of the TSP distribution this methodology leads always to a solution. A detailed analysis comparing the beta and TSP distribution based on their PERT means and variances is presented indicating better results for the second.Abstract.The aim of this paper is to include the Two-Sided Power (TSP) distribution in the PERT methodology making use of the advantages that this four-parameter distribution offers. In order to be completely determined, a distribution of this type needs, the same as the beta distribution, a new datum apart from the three usual values a (pessimistic), m (most likely) and b (optimistic). To solve this question, when using the beta distribution in the PERT context, we are looking for the maximum similarity with the normal and so it is required that the distribution has the same variance as the normal or its same kurtosis, giving rise to the constant variance and mesokurtic families, respectively. Nevertheless, while this approach can be only applied to the beta distribution for some values in the range of the standardized mode, in the case of the TSP distribution this methodology leads always to a solution. A detailed analysis comparing the beta and TSP distribution based on their PERT means and variances is presented indicating better results for the second.

An Elicitation Procedure for the Generalized Trapezoidal Distribution with a Uniform Central Stage

Recent advances in computation technology for decision/simulation and uncertainty analyses have revived interest in the triangular distribution and its use to describe uncertainty of bounded input phenomena. The trapezoidal distribution is a generalization of the triangular distribution that allows for the specification of the modal value by means of a range of values rather than a single point estimate. Whereas the trapezoidal and the triangular distributions are restricted to linear geometric forms in the successive stages of the distribution, the generalized trapezoidal (GT) distribution allows for a nonlinear behavior at its tails and a linear incline (or decline) in the central stage. In this paper we develop two novel elicitation procedures for the parameters of a special case of the GT family by restricting ourselves to a uniform (horizontal) central stage in accordance with the central stage of the original trapezoidal distribution.

Decomposable financial laws and profitability

An important feature of some financial laws is the decomposability property. This is a theoretical issue for a financial law admitting that the cash flow does not change when the economic subject disinvests and immediately re-invests a capital. Decomposable laws are exponential. In the recent past, the notion of decomposability has been generalized, modelling non homogeneity of the time in financial processes by the action of triangular t-conorms over the times. In this more general setting, our aim is to compare and measure the advantages or disadvantages that the economic subject obtains when he interrupts a flow.

Measuring Impatience in Intertemporal Choice.

In general terms, decreasing impatience means decreasing discount rates. This property has been usually referred to as hyperbolic discounting, although there are other discount functions which also exhibit decreasing discount rates. This paper focuses on the measurement of the impatience associated with a discount function with the aim of establishing a methodology to compare this characteristic for two different discount functions. In this way, first we define the patience associated with a discount function in an interval as its corresponding discount factor and consequently we deduce that the impatience at a given moment is the corresponding instantaneous discount rate. Second we compare the degree of impatience of discount functions belonging to the same or different families, by considering the cases in which the functions do or do not intersect.

Markowitz's model with Euclidean vector spaces

In this paper a new approach of the Markowitzs model is presented. Indeed, using an inner product, a quantitative and explicit solution for optimal portfolio selection is given. To do this, a scalar product is defined in which allows us to calculate the composition of the optimal portfolio and the variance for a given expected return by means of the distance between the subspace of feasible solutions and the origin of the affine space.

Valuation Fuzzy Soft Sets: A Flexible Fuzzy Soft Set Based Decision Making Procedure for the Valuation of Assets

Zadeh’s fuzzy set theory for imprecise or vague data has been followed by other successful models, inclusive of Molodtsov’s soft set theory and hybrid models like fuzzy soft sets. Their success has been backed up by applications to many branches like engineering, medicine, or finance. In continuation of this effort, the purpose of this paper is to put forward a versatile methodology for the valuation of goods, particularly the assessment of real state properties. In order to reach this target, we develop the concept of (partial) valuation fuzzy soft set and introduce the novel problem of data filling in partial valuation fuzzy soft sets. The use of fuzzy soft sets allows us to quantify the qualitative attributes involved in an assessment context. As a result, we illustrate the effectiveness and validity of our valuation methodology with a real case study that uses data from the Spanish real estate market. The main contribution of this paper is the implementation of a novel methodology, which allows us to assess a large variety of assets where data are heterogeneous. Our technique permits to avoid the appraiser’s subjectivity (exhibited by practitioners in housing valuation) and the well-known disadvantages of some alternative methods (such as linear multiple regression).

Intertemporal choice and nonadditive capitalization functions

Many papers on finance are interested in studying the preferences of a certain group of individuals about the choice of several rewards available at different time instants. Usually these works are conducted from an experimental point of view by means of samples to be passed to a control group. One of the most important issues in this research is nonadditivity when describing the behavior in experimental intertemporal choice. For instance, subadditivity in behavioral finance means that a certain subject prefers to divide the duration of an investment as many times as possible because this choice leads to an increase in profitability. Another context is medical research on impulsivity and loss of self‐control in drug‐dependent patients because there is a relationship between impulsive decision‐making in intertemporal choice and estimation of time duration. Here subadditivity appears when administering some drugs in a group of substance abusers because they can feel a slight improvement when the same dose is divided into several parts. The problem arising here is how to measure the degree of subadditivity or superadditivity perceived by a group of individuals who are not experts in finance or medicine, respectively. So, our research will be addressed from a nonlinearity of time‐perception perspective.

THE GENERALIZED BIPARABOLIC DISTRIBUTION

Beta distributions have been applied in a variety of fields in part due to its similarity to the normal distribution while allowing for a larger flexibility of skewness and kurtosis coverage when compared to the normal distribution. In spite of these advantages, the two-sided power (TSP) distribution was presented as an alternative to the beta distribution to address some of its short-comings, such as not possessing a cumulative density function (cdf) in a closed form and a difficulty with the interpretation of its parameters. The introduction of the biparabolic distribution and its generalization in this paper may be thought of in the same vein. Similar to the TSP distribution, the generalized biparabolic (GBP) distribution also possesses a closed form cdf, but contrary to the TSP distribution its density function is smooth at the mode. We shall demonstrate, using a moment ratio diagram comparison, that the GBP distribution provides for a larger flexibility in skewness and kurtosis coverage than the beta distribution when restricted to the unimodal domain. A detailed mean-variance comparison of GBP, beta and TSP distributions is presented in a Project Evaluation and Review Technique (PERT) context. Finally, we shall fit a GBP distribution to an example of financial European stock data and demonstrate a favorable fit of the GBP distribution compared to other distributions that have traditionally been used in that field, including the beta distribution.

Observed and Normative Discount Functions in Addiction and other Diseases

The aim of this paper is to find a suitable discount function able to describe the progression of a certain addiction or disease under treatment as a discounting process. In effect, a certain indicator related to a disease decays over time in a manner which is mathematically similar to the way in which discounting has been modeled. We analyze the discount functions observed in experiments which study addictive and other problematic behaviors as well as some alternative hyperbola-like discount functions in order to fit the patience exhibited by the subject after receiving the treatment. Additionally, it has been experimentally found that people with addiction display high rates of discount (impatience) and preference reversals (dynamic inconsistency). This excessive discounting must be correctly modeled by a suitable discount function, otherwise, it can become a trans-disease process underlying addiction and other disorders. The (generalized) exponentiated hyperbolic discount function is proposed to describe the progression of a disease with respect to the treatment, since it maintains the property of inconsistency by exhibiting a decreasing discount rate after an initial period in which the opposite occurs.