Fuzzy interval net present value

In this paper we conjugate the operative usability of the net present value with the capability of the fuzzy and the interval approaches to manage uncertainty. Our fuzzy interval net present value can be interpreted, besides the usual present value of an investment project, as the present value of a contract in which the buyer lets the counterpart the possibility to release goods/services for money amounts that can vary, at time instants that can also vary. The buyer can reduce the widths of these variations by paying a cost. So, it is "natural" to represent the good/service money amounts and the time instants by means of triangular fuzzy numbers, and the cost of the buyer as a strictly increasing function of the level a in [0, 1] associated to the generic cut of the fuzzy interval net present value. As usual, the buyer is characterized by a utility function, depending on a and on the cost, that he/she has to maximize. As far the interest rates regard, we assume that the economic operators are only able to specify a variability range for each of the considered period interest rate. So, we represent the interest rates by means of interval numbers. Besides proposing our model, we formulate and solve the programming problems which have to be coped with to determine the extremals of the cut of the fuzzy interval net present value, and we deal with some questions related to the utility function of the buyer.net present value, fuzzy set theory, interval number theory, alpha-cut, utility function

Financial trading systems: Is recurrent reinforcement the via?

In this paper we propose a financial trading system whose trading strategy is developed by means of an artificial neural network approach based on a learning algorithm of recurrent reinforcement type. In general terms, this kind of approach consists: first, in directly specifying a trading policy based on some predetermined investorâs measure of profitability; second, in directly setting the financial trading system while using it. In particular, with respect to the prominent literature, in this contribution: first, we take into account as measure of profitability the reciprocal of the returns weighted direction symmetry index instead of the wide-spread Sharpe ratio; second, we obtain the differential version of the measure of profitability we consider, and obtain all the related learning relationships; third, we propose a simple procedure for the management of drawdown-like phenomena; finally, we apply our financial trading approach to some of the most prominent assets of the Italian stock market.Financial trading system, recurrent reinforcement learning, no-hidden-layer perceptron model, returns weighted directional symmetry measure, gradient ascent technique, Italian stock market.

What Sequences obey Benford's Law ?

We propose a new necessary and sufficient condition to test whether a sequence is Benford (base-b) or not and apply this characterization to some kinds of sequences (re)obtaining some well known results, as the fact that the sequence of powers of 2 is Benford (base-10).Benford's law, equidistributed sequences, ergodic endomorphisms

Particle Swarm Optimization with non-smooth penalty reformulation for a complex portfolio selection problem

In the classical model for portfolio selection the risk is measured by the variance of returns. It is well known that, if returns are not elliptically distributed, this may cause inaccurate investment decisions. To address this issue, several alternative measures of risk have been proposed. In this contribution we focus on a class of measures that uses information contained both in lower and in upper tail of the distribution of the returns. We consider a nonlinear mixed-integer portfolio selection model which takes into account several constraints used in fund management practice. The latter problem is NP-hard in general, and exact algorithms for its minimization, which are both effective and efficient, are still sought at present. Thus, to approximately solve this model we experience the heuristics Particle Swarm Optimization (PSO). Since PSO was originally conceived for unconstrained global optimization problems, we apply it to a novel reformulation of our mixed-integer model, where a standard exact penalty function is introduced.Portfolio selection, coherent risk measure, fund management constraints, NP-hard mathematical programming problem, PSO, exact penalty method, SP100 index's assets.

Average Rate of Downlink Heterogeneous Cellular Networks over Generalized Fading Channels - A Stochastic Geometry Approach

In this paper, we introduce an analytical framework to compute the average rate of downlink heterogeneous cellular networks. The framework leverages recent application of stochastic geometry to other-cell interference modeling and analysis. The heterogeneous cellular network is modeled as the superposition of many tiers of Base Stations (BSs) having different transmit power, density, path-loss exponent, fading parameters and distribution, and unequal biasing for flexible tier association. A long-term averaged maximum biased-received-power tier association is considered. The positions of the BSs in each tier are modeled as points of an independent Poisson Point Process (PPP). Under these assumptions, we introduce a new analytical methodology to evaluate the average rate, which avoids the computation of the Coverage Probability (Pcov) and needs only the Moment Generating Function (MGF) of the aggregate interference at the probe mobile terminal. The distinguishable characteristic of our analytical methodology consists in providing a tractable and numerically efficient framework that is applicable to general fading distributions, including composite fading channels with small- and mid-scale fluctuations. In addition, our method can efficiently handle correlated Log-Normal shadowing with little increase of the computational complexity. The proposed MGF-based approach needs the computation of either a single or a two-fold numerical integral, thus reducing the complexity of Pcov-based frameworks, which require, for general fading distributions, the computation of a four-fold integral.Comment: Accepted for publication in IEEE Transactions on Communications, to appea

A fuzzy-based scoring rule for author ranking

The measurement of the quality of research has reached nowadays an increasing interest not only for scientific reasons but also for the critical problem of researchers' ranking, due to the lack of grant assignments. The most commonly used approach is based on the so-called $h$-index, even if the current literature debated a lot about its pros and cons. This paper, after a brief review of the $h$-index and of alternative models, focuses on the characterization and the implementation of a modified scoring rule approach by means of a fuzzy inference system a là Sugeno.Research evaluation, bibliometrics, author ranking, $h$-index, scoring rules, fuzzy inference system.

An Artificial Neural Network technique for on-line hotel booking

In this paper the use of Artificial Neural Networks (ANNs) in on-line booking for hotel industry is investigated. The paper details the description, the modeling and the resolution technique of on-line booking. The latter problem is modeled using the paradigms of machine learning, in place of standard `If-Then-Else' chains of conditional rules. In particular, a supervised three layers MLP neural network is adopted, which is trained using information from previous customers' reservations. Performance of our ANN is analyzed: it behaves in a quite satisfactory way in managing the (simulated) booking service in a hotel. The customer requires single or double rooms, while the system gives as a reply the confirmation of the required services, if available. Moreover, we highlight that using our approach the system proposes alternative accommodations (from two days in advance to two days later with respect to the requested day), in case rooms or services are not available. Numerical results are given, where the effectiveness of the proposed approach is critically analyzed. Finally, we outline guidelines for future research.On-line booking; hotel reservation; machine learning; supervised multilayer perceptron networks

Price Forecasting for Bitcoin: Linear Regression and SVM approaches

A long term analysis for the most renowned crypto asset (namely Bitcoin) is considered. Bitcoin has currently the largest market capitalization among the crypto assets, and in the last years has steadily attracted the attention of both private and institutional investors. Since 2008 Bitcoin price has always experienced high volatility, too, which earned it the title of risky asset in the literature of FinTech. Hence, practitioners have stressed the key role of robust models to reliably predicting its value, not to mention the relevance of a comparative analysis with safe haven assets as silver and gold. This paper focuses on a couple of approaches to predict long term Bitcoin price. Basically the first one relies on more standard regression and linear models. Our second proposal is conversely based on applying a Support Vector Machine (SVM), in the class of Machine Learning (ML) methods, which do not require any of the assumptions typically needed by solvers for standard regression problems. We remark that both the above proposals are inherently data-driven

Windowed Decoding of Protograph-based LDPC Convolutional Codes over Erasure Channels

We consider a windowed decoding scheme for LDPC convolutional codes that is based on the belief-propagation (BP) algorithm. We discuss the advantages of this decoding scheme and identify certain characteristics of LDPC convolutional code ensembles that exhibit good performance with the windowed decoder. We will consider the performance of these ensembles and codes over erasure channels with and without memory. We show that the structure of LDPC convolutional code ensembles is suitable to obtain performance close to the theoretical limits over the memoryless erasure channel, both for the BP decoder and windowed decoding. However, the same structure imposes limitations on the performance over erasure channels with memory.Comment: 18 pages, 9 figures, accepted for publication in the IEEE Transactions on Information Theor

Cumulative Prospect Theory portfolio selection

We introduce elements of Cumulative Prospect Theory into the portfolio selection problem and then compare stock portfolios selected under the behavioral approach with those selected according to classical approaches, such as Mean Variance and Mean Absolute Deviation ones. The mathematical programming problem associated to the behavioral portfolio selection is highly non-linear and non-differentiable; for these reasons it is solved using a Particle Swarm Optimization approach. An application to the STOXX Europe 600 equity market is performed.We introduce elements of Cumulative Prospect Theory into the portfolio selection problem and then compare stock portfolios selected under the behavioral approach with those selected according to classical approaches, such as Mean-Variance and Mean Absolute Deviation ones. The mathematical programming problem associated to the behavioral portfolio selection is highly non-linear and non-differentiable; for these reasons, it is solved using a Particle Swarm Optimization approach. An application to the STOXX Europe 600 equity market is performed