Purpose: Providing an analytical approach to minimize risk to a situation that traders deal with model risk, as a financial risk arises by choosing an Approximation model, for the underlying securities status in financial estimates. Methodology: Improving the standard binomial pricing model and using the equivalence portfolio mechanism in a particular incomplete market situation which traders are uncertain about the actual status space of the stock binomial process. Findings: From a research aspect, a model of Approximation was provided and generalized with different hypotheses that minimizes the risk of the model for pricing call options. From an applied practical aspect, the results give to financial institutions the outlook to predict a mechanism to moderate excessive volatilities in the markets related to options. Originality/Value: The study of the model risk is performed by maintaining the simple framework and elegance of the binomial model and then it is proved that by defining the optimality in the sense of minimum mean-square errors, the choice of an optimal Approximation model is possible. In addition, the implementation and efficiency of the method for the multi-period model are explained.

Let P1  and P 2 be two gamma independent populations that Pi has unknown scale parameter qi and common and known shape parameter a . Suppose that X1 and X2 are drown from P1 and P2, respectively, and the population corresponding to X (1)=min (X1, X2) and X (2)=max (X1 ,X2) is selected. The aim of this paper is to find the optimal decisions for the scale parameters qM and qJ from the selected gamma population under a generalized scale invariant loss function. To do this, we obtain admissible and inadmissible decisions of the form cX (1) or cX (2) in a subclass of invariant decisions qM or qJ. Moreover, Bayes and generalized Bayes decisions of qM and qJ are obtained and we show that these decisions are admissible. We apply our results for censored data and also for Weibull and Rayleigh distributions.

Flood protection must be taken into account in almost all development projects. Owing to the fact that hazards associated with flooding (such as disruption of services, health impacts, famine and disease), the new approaches in flood risk management are needed. Therefore, it is essential that the selection of flood management option by cost-benefit viewpoint to be shifted to the selection of flood management option by considering the economic, technical, social, and environmental aspects. Due to the complexity of these challenges, water resources planners require a holistic, adaptive, incremental, and sustainable decision-making process, where multiple non-commensurate, competing, and often conflicting objectives (criteria) must be addressed and reconciled. During the past several decades, multi criteria decision making (MCDM), by its philosophical underpinning and the theory, methodology, and practice that have been developed on the basis of its holistic philosophy, has served as a harmonizing agent in technology, society, and policy. Thus, formidability of this method in addressing the flood management alternatives challenges is undeniable fact. In this paper, there are seven flood management measures in Gorganrood Watershed flood management project, including: conservation of natural condition, Golestan Reservoir management, levee construction, diversions-canal construction, flood forecasting and warning system and flood insurance. Prioritization of the alternatives is in demand of evaluation criteria. Each alternative would be prioritized based upon proposed MCDMs to investigate the most conclusive alternative. The flood management project is ranked based on eleven criteria, including: expected average number of casualties, recovery rate, gradual rate, expected annual damage, safety feeling, employment rate, public participation, landscape protection, wildlife habitat conservation, water quality conservation and technical feasibility and performance. These criteria have been classified into four main groups as social, economic, environmental and technical features. Compromise Programming model (CP) is employed to rank these seven alternatives which are compared with simple additive weighted model (SAW). SAW is known to be common method, which is accepted in many researches due to its simplicity. In this method, alternatives are assessed with respect to each criterion, whilst CP defines the best solution as the one in the set of efficient solutions whose point is at the least distance from an ideal point and the aim is to obtain a solution that is as close as possible to some ideal alternative. The results show that by increasing the value of P parameter, the CP model emphasizes on the importance of recovery rate, expected average number of casualties and safety feeling, which categorized in economic, social and technical feasibility, respectively. This result is obtained by assessing the changes in criteria weights while the P parameter increase from P=1 to P=¥. In the proposed model, integration of a flood warning system and flood insurance was chosen as the most conclusive alternative for flood hazard mitigation. This alternative is a combination of a pre and post disaster action. In contrast, SAW model is unable to highlight or discriminate between the criteria. One of the criticisms over MCDM states that different techniques may yield different results when applied to the same problem. An analyst looks for a solution that is closest to the ideal, in which alternatives are evaluated according to all established criteria. Therefore, it is necessary to compare the MCDMs plus assessment of subjectivity with sensitivity analysis of input data. In this study, sensitivity analysis was performed to examine the response of alternatives when the criteria weights changed to its minimum and maximum values. The results show that the CP model has less sensitivity to changes in criteria weights. Due to considering the ideal solution distance, CP model has more sensitivity to economic and technical criteria in comparison with environmental and social criteria. Although SAW model has less sensitivity to changes in criteria weights, it makes no priority between criteria even in sensitivity analysis. It is observed that the change of the MCDM methods produces differences in the final ranking of the alternatives. The discrepancy that appears between the rankings obtained by different MCDM methods, highly depended on the difference in their mathematical modeling while solving a decision problem. Thus, the main focus must lie on the selection of the most appropriate MCDM method to be adopted, not to mention that proper structuring of the decision problem, considering the relevant criteria and decision alternatives are imperative facts on this issue.

In this paper, we introduce the concept of best proximal contraction theorems in non-Archimedean fuzzy metric space for two mappings and prove some proximal theorems. As a consequence, it provides the existence of an optimal approximate solution to some equations which contains no solution. The obtained results extend further the recently development proximal contractions in non-Archimedean fuzzy metric spaces and famous Banach contraction principle.

In this article, Ritz Approximation have been employed to obtain the numerical solutions of a class of the fractional optimal control problems based on the Caputo fractional derivative. Using polynomial basis functions, we obtain a system of nonlinear algebraic equations. This nonlinear system of equation is solved and the coefficients of basis polynomial are derived. The convergence of the numerical solution is investigated. Some numerical examples are presented which illustrate the theoretical results and the performance of the method.

Choosing the right basket of stocks that has the highest returns has always been a concern for real and legal investors. Therefore, the present study, by developing Gordon's view and using mixed fuzzy multi-criteria decision making, identifies effective factors and determines the relative weight of dividends, discount rate, and dividend growth rate. The purpose of this research is to develop a multi-criteria decision-making model to provide investors with the criteria to obtain higher returns by choosing the optimal portfolio of portfolios. The purpose of this study is to develop a multi-criteria decision making model in order to provide criteria for investors in order to obtain higher returns by selecting a more optimal portfolio of portfolios. The general objective of the research is to determine the effective measures on stock selection in Tehran Stock Exchange using an integrated model (DEAMATEL). The order of effectiveness and efficacy of the main metrics with Dimetal has shown that the profit criterion has the most interaction with other criteria. Then, in terms of MPO, Market, Risk, Growth criteria, they are ranked next in terms of interacting with other criteria.

In this paper, a numerical method for solving stochastic optimal control problem by using Markov chain Approximation method has presented. The basic idea of the Markov chain Approximation method is to approximate the original controlled process by an appropriate controlled Markov chain on a finite state space.Also, we need to approximate the original cost function by one which is appropriate for the approximating chain. These Approximations should be chosen such that a good numerical Approximation to the associated optimal control problem can be obtained, which means the conditional mean and covariance of the changes in state of the chain are proportional to the local mean drift and covariance for the original process. The finite difference Approximations are used to the construction of locally consistent approximating Markov chain, the coefficients of the resulting discrete equation can serve as the desired transition probabilities and interpolation interval.

The optimal Power Flow is one of the fundamental problems in power system analyses. Some essential studies in power system operation and planning typically require a large number of repetitive OPF solutions. In these analyses, the convergence speed of the OPF solutions beside their accuracy are two key objects. The full ACOPF is accurate, but takes long solution time. The DCOPF is a simple Approximation of OPF that is very fast but is not so accurate. This paper presents a method to improve the accuracy of DCOPF, based on evaluating some nodal shares of transmission losses. Like the previous DCOPF, the Modified DCOPF is derived from a non-iterative DC power flow, and thus its solution requires no long run time. Moreover, it can simply be realized in the form of Lagrange representation, makes it possible to be considered as some constraints in the body of any bilevel optimization problem, with its internal level including the OPF satisfaction. The efficiency of the Modified DCOPF is illustrated through implementing on three test cases (IEEE 30 & 118 Bus test systems and Iran 2006 Transmission Network) and comparing the results (generation levels, line flows, and voltage angles) with the conventional DCOPF and full ACOPF.