Stochastic logistic fuzzy maps for the construction of integrated multirates scenarios in the financing of infrastructure projects

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.In general, the development of economic infrastructure systems requires a behavioural comprehensive analysis of different financial variables or rates to establish its long-term success with regards to the Equity Internal Rate of Return (EIRR) expectation. For this reason, several financial organizations have developed economic scenarios supported by computational techniques and models to identify the evolution of these financial rates. However, these models and techniques have shown a series of limitations with regard to the financial management process and its impact on EIRR over time. To address these limitations in an inclusive way, researchers have developed different approaches and methodologies focused on the development of financial models using stochastic simulation methods and computational intelligence techniques. This paper proposes a Stochastic Fuzzy Logistic Model (S-FLM) inspired by a Fuzzy Cognitive Map (FCM) structure to model financial scenarios. Where the input consists in financial rates that are characterized as linguistic rates through a series of adaptive logistic functions. The stochastic process that explains the behaviour of the financial rates over time and their partial effects on EIRR is based on a Monte Carlo sampling process carried out on the fuzzy sets that characterize each linguistic rate. The S-FLM was evaluated by applying three financing scenarios to an airport infrastructure system (pessimistic, moderate/base, optimistic), where it was possible to show the impact of different linguistic rates on the EIRR. The behaviour of the S-FLM was validated using three different models: (1) a financial management tool; (2) a general FCM without pre-loaded causalities among the variables; and (3) a Statistical S-FLM model (S-FLMS), where the causalities between the concepts or rates were obtained as a result of an independent effects analysis applying a cross modelling between variables and by using a statistical multi-linear model (statistical significance level) and a multi-linear neural model (MADALINE). The results achieved by the S-FLM show a higher EIRR than expected for each scenario. This was possible due to the incorporation of an adaptive multi-linear causality matrix and a fuzzy credibility matrix into its structure. This allowed to stabilize the effects of the financial variables or rates on the EIRR throughout a financing period. Thus, the S-FLM can be considered as a tool to model dynamic financial scenarios in different knowledge areas in a comprehensive manner. This way, overcoming the limitations imposed by the traditional computational models used to design these financial scenarios

Statistical inference for multivariate extremes via a geometric approach

A geometric representation for multivariate extremes, based on the shapes of scaled sample clouds in light-tailed margins and their so-called limit sets, has recently been shown to connect several existing extremal dependence concepts. However, these results are purely probabilistic, and the geometric approach itself has not been fully exploited for statistical inference. We outline a method for parametric estimation of the limit set shape, which includes a useful non/semi-parametric estimate as a pre-processing step. More fundamentally, our approach provides a new class of asymptotically-motivated statistical models for the tails of multivariate distributions, and such models can accommodate any combination of simultaneous or non-simultaneous extremes through appropriate parametric forms for the limit set shape. Extrapolation further into the tail of the distribution is possible via simulation from the fitted model. A simulation study confirms that our methodology is very competitive with existing approaches, and can successfully allow estimation of small probabilities in regions where other methods struggle. We apply the methodology to two environmental datasets, with diagnostics demonstrating a good fit

Extremal financial risk models and portfolio evaluation

It is difficult to find an existing single model which is able to simultaneously model exceedances over thresholds in multivariate financial time series. A new modeling approach, which is a combination of max-stable processes, GARCH processes, and Markov processes, is proposed. Combining Markov processes and max-stable processes defines a new statistical model which has the flexibility of modeling cross-sectional tail dependencies between risk factors and tail dependencies across time. The new model also models asymmetric behaviors of negative and positive returns on financial assets. An important application of the proposed method is to calculate value at risk (VaR) and evaluate portfolio combinations under VaR constraints. Result comparisons between VaRs based on the new approach and VaRs based on some existing methods such as variance–covariance approach and historical simulation approach suggest that some existing methods substantially underestimate the risks during recession and expansion time