An approach for linguistic multi-attribute decision making based on linguistic many-valued logic

There are various types of multi-attribute decision-making (MADM) problems in our daily lives and decision-making problems under uncertain environments with vague and imprecise information involved. Therefore, linguistic multi-attribute decision-making problems are an important type studied extensively. Besides, it is easier for decision-makers to use linguistic terms to evaluate/choose among alternatives in real life. Based on the theoretical foundation of the Hedge algebra and linguistic many-valued logic, this study aims to address multi-attribute decision-making problems by linguistic valued qualitative aggregation and reasoning method. In this paper, we construct a finite monotonous Hedge algebra for modeling the linguistic information related to MADM problems and use linguistic many-valued logic for deducing the outcome of decision making. Our method computes directly on linguistic terms without numerical approximation. This method takes advantage of linguistic information processing and shows the benefit of Hedge algebra

Systematic risk analysis: first steps towards a new definition of beta

We suggest a new model-free definition of the beta coefficient, which plays an important rôle in systematic risk management. This setting, which is based on the existence of trends for financial time series via nonstandard analysis (Fliess M., Join C.: A mathematical proof of the existence of trends in financial time series, Proc. Int. Conf. Systems Theory: Modelling, Analysis and Control, Fes, 2009, online: http://hal.inria.fr/inria-00352834/en/) leads to convincing computer experiments which are easily implementable.Quantitative finance; risk analysis; beta; alpha; trends; technical analysis; estimation techniques; forecasting; abrupt changes; nonstandard analysis.

Utility-Based Hedging of Stochastic Income

In this dissertation, we study and examine utility-based hedging of the optimal portfolio choice problem in stochastic income. By assuming that the investor has a preference governed by negative exponential utility, we a derive a closed-form solution for the indifference price through the pricing methodology based on utility maximization criteria. We perform asymptotic analysis on this closed form solution to develop the analytic approximation for the indifference price and the optimal hedging strategy as a power series expansion involving the risk aversion and the correlation between the income and a traded asset. This gives a fast computation route to assess these quantities and perform our analysis. We implemented the model to perform simulations for the optimal hedging policy and produce the distributions of the hedging error at terminal time over many sample paths histories. In turn, we analyze the performance of the utility-based hedging strategy together with the strategy which arises from employing the traded asset as a substitute for the stochastic income

A model for hedging load and price risk in the Texas electricity market

Energy companies with commitments to meet customers’ daily electricity demands face the problem of hedging load and price risk. We propose a joint model for load and price dynamics, which is motivated by the goal of facilitating optimal hedging decisions, while also intuitively capturing the key features of the electricity market. Driven by three stochastic factors including the load process, our power price model allows for the calculation of closed-form pricing formulas for forwards and some options, products often used for hedging purposes. Making use of these results, we illustrate in a simple example the hedging benefit of these instruments, while also evaluating the performance of the model when fitted to the Texas electricity market

THE REAL-WORLD-SEMANTICS INTERPRETABILITY OF LINGUISTIC RULE BASES AND THE APPROXIMATE REASONING METHOD OF FUZZY SYSTEMS

The real-world-semantics interpretability concept of fuzzy systems introduced in [1] is new for the both methodology and application and is necessary to meet the demand of establishing a mathematical basis to construct computational semantics of linguistic words so that a method developed based on handling the computational semantics of linguistic terms to simulate a human method immediately handling words can produce outputs similar to the one produced by the human method. As the real world of each application problem having its own structure which is described by certain linguistic expressions, this requirement can be ensured by imposing constraints on the interpretation assigning computational objects in the appropriate computational structure to the words so that the relationships between the computational semantics in the computational structure is the image of relationships between the real-world objects described by the word-expressions. This study will discuss more clearly the concept of real-world-semantics interpretability and point out that such requirement is a challenge to the study of the interpretability of fuzzy systems, especially for approaches within the fuzzy set framework. A methodological challenge is that it requires both the computational expression representing a given linguistic fuzzy rule base and an approximate reasoning method working on this computation expression must also preserve the real-world semantics of the application problem. Fortunately, the hedge algebra (HA) based approach demonstrates the expectation that the graphical representation of the rule of fuzzy systems and the interpolation reasoning method on them are able to preserve the real-world semantics of the real-world counterpart of the given application problem

Comparing conditional hedging strategies.

The traditional approach to discriminate amongst two competing hedging strategies is to compare the sample portfolio return variance implied by each strategy. This simple approach suffers from two drawbacks. First, it is an unconditional performance measure which is theoretically not coherent with a dynamic hedging strategy that minimizes the conditional portfolio return variance. Second, estimating unconditional performance over the entire period may not be sufficcient since a strategy with a good unconditional hedging performance may not perform well at a particular point in time. In this paper, I use the Giacomini and White (2006), the Wald, and the Diebold and Mariano (1995) statistical tests in order to conditionally (and as a special case, unconditionally) compare the portfolio return variances implied by two competing hedging strategies. The attractive feature of the conditional perspective is that, in case of rejection of equal conditional hedging effectiveness among two initial strategies, it provides us with a new hedging strategy that selects at each date the initial strategy that will perform the best next period, conditional on current information. An application to several agricultural commodities illustrates the technique. For daily hedging horizons, it is found that most of the time Ederington's (1979) static strategy is superior to more elaborate dynamic strategies. This calls into question earlier results reported in the literature that were based on a much smaller database.GARCH; Hedging; Strategy; Portfolio; Variance; IT; Performance; Time; Tests; Order; Effectiveness; Information; Database;

DESIGNING HEDGE ALGEBRAIC CONTROLLER AND OPTIMIZING BY GENETIC ALGORITHM FOR SERIAL ROBOTS ADHERING TRAJECTORIES

In recent years, the application of hedge algebras in the field of control has been studied. The results show that this approach has many advantages. In additions, industrial robots are being well-developed and extensively used, especially in the industrial revolution 4.0. Accurate control of industrial robots is a class of problems that many scientists are interested in. In this paper, we design a controller based on hedge algebra for serial robots. The control rule is given by linguistic rule base system. The goal is to accurately control the moving robot arm which adheres given trajectories. Optimization of fuzzy parameters for the controller is done by genetic algorithms. The system has been simulated on the Matlab-Simulink software. The simulation results show that the orbital deviation is very small. Moreover, the controller worked well with correct control quality. This result once presents the simplicity and efficiency of the hedge algebras approach to control