An evolving possibilistic fuzzy modeling approach for Value-at-Risk estimation

Maciel, Leandro; Ballini, Rosângela; Gomide, Fernando

doi:10.1016/j.asoc.2017.04.028

Cited by 11 publications

(11 citation statements)

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“…The financial risks of projects are identified simulating the fuzzy system in the search of Bolos et al (2015). It is obvious, that risk plays a key role in financial management, which forced Maciel et al (2017) to research a way to measure risk exposure. As a result, they suggested an evolving possibilistic fuzzy modelling approach to estimate value at risk.…”

Section: Literature Reviewmentioning

confidence: 99%

Behavioural Aspects of the Financial Decision-Making

2019

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Background and Purpose: Behavioural finance is a relatively new, but rapidly evolving field that provides explanations of an economic decision-making by cognitive psychology, conventional economic and financial theory. Behavioural finance searches the influence of psychology on the behaviour of financial practitioners and the subsequent effects on the financial markets. The purpose of the paper is the research on behavioural aspects of financial decision-making as they help explain why and how markets might be inefficient. Design/Methodology/Approach: Fuzzy logic is an excellent tool for working with linguistic variables that are often found when working with behavioural data. Thus, we analyse the financial decision-making process from the perspective of behavioural finance aimed at better understanding of the decision-making process of investors applying the principles of fuzzy logic to solve various financial problems. Results: The results of the study indicate that fuzzy logic is applicable when solving problems of financial management and financial decision-making problems. The urgency of the fuzzy logic application for managerial and financial decisions should be emphasized. Research in this area indicates that in some cases, as in the case of behavioural financing, the use of fuzzy logic is far more suitable than the use of other methods (Peters, Aguiar and Sales). Conclusion: The novelty of the paper is to extend the application of fuzzy sets in the area of financial decision-making. The paper demonstrates that despite the fact, that fuzzy logic is currently used mainly in technical directions, it is applicable also in financial management, especially, in cases where it is necessary to consider the influence of human and the occurrence of linguistic variables.

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Section: Literature Reviewmentioning

confidence: 99%

Behavioural Aspects of the Financial Decision-Making

2019

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“…If rule adding method is not satisfied, then SEFS updates the cluster center and radius of rule R i * according to rule updating method, the formulas in which are based on the sample meanĉ and varianceσ 2 shown in (8)…”

Section: Then A(t) Could Be Updated Bymentioning

confidence: 99%

“…Considering eFSs developed based on generalized fuzzy rules [6], Mahalanobis distance has been used to control the fuzzy rule growth e.g. [7], [8]. Similar to distance based methods, there exists another effective criterion built according to the activation degree (or firing strength).…”

Section: Introductionmentioning

confidence: 99%

“…One is fuzzy rule merging and the other is fuzzy rule pruning. Previous researches such as [8], [14], [16], [24], [27], [29], [30] proposed and used rule simplification criterions such as age, utility to delete clusters which are rarely used. Apart from pruning low utility rules, another desirable approach to simplify the rule base is known as fuzzy rule merging.…”

Section: Introductionmentioning

confidence: 99%

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A Self-Evolving Fuzzy System Which Learns Dynamic Threshold Parameter by Itself

Zeng

2019

IEEE Trans. Fuzzy Syst.

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This paper proposes an online learning algorithm for data streams namely self-evolving fuzzy system (SEFS). Unlike the fixed control parameters commonly used in evolving fuzzy systems, SEFS uses online training errors, which measure the quality of an identified model in presenting the dynamics of the data stream, to set a dynamic threshold automatically for rule generation. This self-tuning parameter, which controls the speed and coverage for fuzzy rule generation, helps SEFS properly deal with the under-fitting/over-fitting problems relying on two facts. (1) Large training errors present an under-fitted model, which is too coarse to represent the highly complicated and rapidly dynamic (e.g. highly nonlinear, non-stationary) behavior of the data segment. Then, finer rules need to be added. (2) Tiny training errors reflect an over-fitted model, which can ideally represent any slight dynamic behavior of the data stream. In this case, coarse rule base should be used. Besides, a L 2 distance based geometric similarity measure is proposed in the rule merging phase. With this similarity measure, SEFS computes the similarity between Gaussian membership functions accurately without making an approximation of the Gaussian membership function beforehand. In addition, a weighted recursive least square algorithm with a variable forgetting factor (VFF-WRLS), which minimizes the mean square of the noise-free posterior error signal, is applied to learn the consequent parameters. Several benchmark examples across both artificial and real-life data sets verify that SEFS has the ability to give better performance compared with many state-of-the-art algorithms.Index Terms-Evolving fuzzy system, recursive least square, online learning, data stream.

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“…A possibilistic portfolio model is proposed in [10] as an expansion of the possibilistic mean-variance model by with VaR constraint and risk-free investment are computed taking the assumption that the expected rate of returns is a fuzzy number. In [11] the authors suggest an evolving possibilistic fuzzy modeling (ePFM) approach to estimate VaR; data from the main global equity market indexes are used to estimate VaR using ePFM and the performance of ePFM is compared with traditional VaR benchmarks producing encouraging results. A growing interest for researches and practitioners is directed to VaR estimation in the case of operational risk, in [12] the intrinsic properties of the data as fuzzy sets are related to the linguistic variables of the observed data (external), allowing an organization to supervise operational VaR over time.…”

Section: Introductionmentioning

confidence: 99%

Value at Risk Based on Fuzzy Numbers

Guerra

Sorini

2020

Axioms

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Value at Risk (VaR) has become a crucial measure for decision making in risk management over the last thirty years and many estimation methodologies address the finding of the best performing measure at taking into account unremovable uncertainty of real financial markets. One possible and promising way to include uncertainty is to refer to the mathematics of fuzzy numbers and to its rigorous methodologies which offer flexible ways to read and to interpret properties of real data which may arise in many areas. The paper aims to show the effectiveness of two distinguished models to account for uncertainty in VaR computation; initially, following a non parametric approach, we apply the Fuzzy-transform approximation function to smooth data by capturing fundamental patterns before computing VaR. As a second model, we apply the Average Cumulative Function (ACF) to deduce the quantile function at point p as the potential loss VaRp for a fixed time horizon for the 100p% of the values. In both cases a comparison is conducted with respect to the identification of VaR through historical simulation: twelve years of daily S&P500 index returns are considered and a back testing procedure is applied to verify the number of bad VaR forecasting in each methodology. Despite the preliminary nature of the research, we point out that VaR estimation, when modelling uncertainty through fuzzy numbers, outperforms the traditional VaR in the sense that it is the closest to the right amount of capital to allocate in order to cover future losses in normal market conditions.

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An evolving possibilistic fuzzy modeling approach for Value-at-Risk estimation

Cited by 11 publications

References 64 publications

Behavioural Aspects of the Financial Decision-Making

Behavioural Aspects of the Financial Decision-Making

A Self-Evolving Fuzzy System Which Learns Dynamic Threshold Parameter by Itself

Value at Risk Based on Fuzzy Numbers

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