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The authors discuss the value of portfolio and Black–Scholes (B–S)-option pricing model in fuzzy environment.

The B–S option pricing model (OPM) is an important role of an OPM in finance. Here, every decision is taken under uncertainty. Due to randomness or vagueness, these uncertainties may be random or fuzzy or both. As the drift µ, the degree of volatility s, interest rate r, strike price k and other parameters of the value of the portfolio V(t), market price S_0 (t) and call option C(t) are not known exactly, so they are treated as positive fuzzy number. Partial expectation of fuzzy log normal distribution is derived. Also the value of portfolio at any time t and the B–S OPM in fuzzy environment are derived. A numerical example of B–S OPM is illustrated.

First, the authors are studying some various paper and some stochastic books.

This is a new technique.

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

Identification in a regression discontinuity (RD) design hinges on the discontinuity in the probability of treatment when a covariate (assignment variable) exceeds a known threshold. If the assignment variable is measured with error, however, the discontinuity in the relationship between the probability of treatment and the observed mismeasured assignment variable may disappear. Therefore, the presence of measurement error in the assignment variable poses a challenge to treatment effect identification. This chapter provides sufficient conditions to identify the RD treatment effect using the mismeasured assignment variable, the treatment status and the outcome variable. We prove identification separately for discrete and continuous assignment variables and study the properties of various estimation procedures. We illustrate the proposed methods in an empirical application, where we estimate Medicaid takeup and its crowdout effect on private health insurance coverage.

In this paper, a mixture of exponential and Rayleigh distributions in the proportions α and 1 − α and all the parameters in the mixture distribution are estimated based on fuzzy data.

The methods such as maximum likelihood estimation (MLE) and method of moments (MOM) are applied for estimation. Fuzzy data of triangular fuzzy numbers and Gaussian fuzzy numbers for different sample sizes are considered to illustrate the resulting estimation and to compare these methods. In addition to this, the obtained results are compared with existing results for crisp data in the literature.

The application of fuzziness in the data will be very useful to obtain precise results in the presence of vagueness in data. Mean square errors (MSEs) of the resulting estimators are computed using crisp data and fuzzy data. On comparison, in terms of MSEs, it is observed that maximum likelihood estimators perform better than moment estimators.

Classical methods of obtaining estimators of unknown parameters fail to give realistic estimators since these methods assume the data collected to be crisp or exact. Normally, such case of precise data is not always feasible and realistic in practice. Most of them will be incomplete and sometimes expressed in linguistic variables. Such data can be handled by generalizing the classical inference methods using fuzzy set theory.

While there exist many surveys on the use stochastic frontier analysis (SFA), many important issues and techniques in SFA were not well elaborated in the previous surveys, namely, regular models, copula modeling, nonparametric estimation by Grenander’s method of sieves, empirical likelihood and causality issues in SFA using regression discontinuity design (RDD) (sharp and fuzzy RDD). The purpose of this paper is to encourage more research in these directions.

A literature survey.

While there are many useful applications of SFA to econometrics, there are also many important open problems.

This is the first survey of SFA in econometrics that emphasizes important issues and techniques such as copulas.

This paper deals with the discrimination problem of the states which involve two types of uncertainty: “randomness” and “fuzziness.” This problem is very important in the fields of soft science such as management science, sociology, eta, since the object of discrimination involves these types of uncertainty. In this paper, we propose a discrimination system of fuzzy states on a probability space and derive the decision rule which minimizes the average of error probability of discrimination. In our formulation of the discrimination system there exists the case that a large number of observations does not necessarily make the average of error probability small, so that an index for decision of an upper limit of number of observations is also derived.

In this paper, new procedures for a fuzzy Markov reward model are introduced to find the reliability measures.

It is supposed that the introduced system consisted of n identical units connected in parallel and each unit has m different types of failures. Also, each unit of the system is allowed to have d levels of degradation from a working state to complete failure. Non-homogeneous Markov reward model is used to construct the system of differential equations of the model. Procedures are proposed to obtain reliability measures of the model under considering that the failure and repair rates of the systems unit are fuzzy. An application is constructed to analyze a system of 2-unit, and results are shown graphically.

Non-homogeneous Markov reward model is used to construct the system of differential equations of the model.

All papers in literature assumed Markov reward model with deterministic parameters. In this paper, a generalization of classical Markov reward model is introduced.

Provides an overview of major developments pertaining to generalized information theory during the lifetime of Kybernetes. Generalized information theory is viewed as a collection of concepts, theorems, principles, and methods for dealing with problems involving uncertainty‐based information that are beyond the narrow scope of classical information theory. Introduces well‐justified measures of uncertainty in fuzzy set theory, possibility theory, and Dempster‐Shafer theory. Shows how these measures are connected with the classical Hartley measure and Shannon entropy. Discusses basic issues regarding some principles of generalized uncertainty‐based information.

The purpose of this paper is to assess model risk with regard to wind energy output in monthly cash flow models for the purpose of valuation and risk assessment of wind farm investments, where only a few approaches exist in the literature.

This paper focuses on the risk-return characteristics of this investment from the perspective of private and institutional investors and takes into account several risks, in particular the resource risk related to the uncertainty of the monthly wind energy produced. To this end, this paper presents different approaches for modeling monthly wind power output and assesses the impact of three selected models with different properties on the investment’s risk-return characteristics by means of a stochastic discounted cash flow model. In addition, the model considers the possibility of a joint operation of the wind farm with a pumped hydro storage system to reduce risk and improve profits.

The results show that the (non-)consideration of seasonality of the monthly wind energy produced considerably influences the risk-return characteristics, but that principal developments dependent on input parameters and model variables remain similar.

This paper contributes to the literature by presenting different approaches for modeling the monthly wind energy produced based on direct models of the wind energy output, which are rare in the existing literature. Further, their impact on risk-return characteristics of a wind farm investment is analyzed, and thus, related model risk is assessed.