FATWA COORDINATION IN MALAYSIA: A LITERATURE REVIEW

Fatwa coordination in Malaysia are non-ending issues due to certain factors whereas debated by many scholars. The issues of non-coordination or inconsistency of fatwa between the State Fatwa Committee and the Muzakarah Committee of the National Council for Islamic Religious Affairs in Malaysia discussed by many reviewers as well as its impact on the community and the fatwa institution itself.Hence, this article aims to highlight past research related to the issue of fatwa coordination in Malaysia.The approach adopted is the method content analysis of past studies. The analysis of this literature uses thematic method approach in understanding selected articles based on random systems and the use of keywords in relation to fatwa coordination. Synthesis analysis carried out has resulted in six (6) themes consisting of factors of inconsistency, impact of inconsistency, importance of coordination, resolution of inconsistencies, minimization of inconsistency and the role of the Muzakarah Committee as the national fatwa institution. Thematic reviews give the advantages of the structured aspects of the discussion to the studies carried out by past surveyors.

Krylov Methods for Large Sparse Systems: A Comprehensive Overview

In this paper are analyzed behavior and properties for different Krylov methods applied in different categories of problems. These categories often include PDEs, econometrics and network models, which are represented by large sparse systems. For our empirical analysis are taken into consideration size, the density of non-zero elements, symmetry/un-symmetry, eigenvalue distribution, also well/ill-conditioned and random systems. Convergence, approximation error and residuals are compared for the full version of methods, some restarted methods and preconditioned methods. Two preconditioners are considered respectively, ILU(0) and IC(0) by using at least five preconditioning techniques. In each case, empirical results show which technique is best to use based on properties of the system and are backed up by general theoretical information already found on Krylov space methods.

Optimizing Expected Shortfall under an ℓ1 Constraint—An Analytic Approach

Expected Shortfall (ES), the average loss above a high quantile, is the current financial regulatory market risk measure. Its estimation and optimization are highly unstable against sample fluctuations and become impossible above a critical ratio r=N/T, where N is the number of different assets in the portfolio, and T is the length of the available time series. The critical ratio depends on the confidence level α, which means we have a line of critical points on the α−r plane. The large fluctuations in the estimation of ES can be attenuated by the application of regularizers. In this paper, we calculate ES analytically under an ℓ1 regularizer by the method of replicas borrowed from the statistical physics of random systems. The ban on short selling, i.e., a constraint rendering all the portfolio weights non-negative, is a special case of an asymmetric ℓ1 regularizer. Results are presented for the out-of-sample and the in-sample estimator of the regularized ES, the estimation error, the distribution of the optimal portfolio weights, and the density of the assets eliminated from the portfolio by the regularizer. It is shown that the no-short constraint acts as a high volatility cutoff, in the sense that it sets the weights of the high volatility elements to zero with higher probability than those of the low volatility items. This cutoff renormalizes the aspect ratio r=N/T, thereby extending the range of the feasibility of optimization. We find that there is a nontrivial mapping between the regularized and unregularized problems, corresponding to a renormalization of the order parameters.