Variable modeling of fuzzy phenomena with industrial applications

Includes abstract. Includes bibliographical references (leaves 98-100)

Pricing options in a fuzzy environment

Includes abstract.Includes bibliographical references (leaves 114-116).Although Fuzzy Logic is not new, it is however only since 2004 that an axiomatic theory has been created that has all the desirable effects of Fuzzy Logic. This theory, named Credibility theory was proposed by Dr. Liu. Within this thesis we aim to utilize credibility theory to model the psychological impacts of market participants on European options. Specifically this is done by modifying the approach that was originally taken by Black and Scholes. The Hew model, which is known as the fuzzy drift parameter model, begins by replacing the deterministic drift within Brownian motion with a fuzzy parameter. This fuzzy parameter models the psychological impacts of market participants. Naturally as we are dealing in Chance theory 1 the risk neutral dynamics change from that of Black and Scholes and thus so does the price of European call options

Fuzzy FMECA analysis of radioactive gas recovery system in the SPES experimental facility

Selective Production of Exotic Species is an innovative plant for advanced nuclear physic studies. A radioactive beam, generated by using an UCx target-ion source system, is ionized, selected and accelerated for experimental objects. Very high vacuum conditions and appropriate safety systems to storage exhaust gases are required to avoid radiological risk for operators and people. In this paper, Failure Mode, Effects, and Criticality Analysis of a preliminary design of high activity gas recovery system is performed by using a modified Fuzzy Risk Priority Number to rank the most critical components in terms of failures and human errors. Comparisons between fuzzy approach and classic application allow to show that Fuzzy Risk Priority Number is able to enhance the focus of risk assessments and to improve the safety of complex and innovative systems such as those under consideration

Scenarios, probability and possible futures

This paper provides an introduction to the mathematical theory of possibility, and examines how this tool can contribute to the analysis of far distant futures. The degree of mathematical possibility of a future is a number between O and 1. It quantifies the extend to which a future event is implausible or surprising, without implying that it has to happen somehow. Intuitively, a degree of possibility can be seen as the upper bound of a range of admissible probability levels which goes all the way down to zero. Thus, the proposition `The possibility of X is Pi(X) can be read as `The probability of X is not greater than Pi(X).Possibility levels offers a measure to quantify the degree of unlikelihood of far distant futures. It offers an alternative between forecasts and scenarios, which are both problematic. Long range planning using forecasts with precise probabilities is problematic because it tends to suggests a false degree of precision. Using scenarios without any quantified uncertainty levels is problematic because it may lead to unjustified attention to the extreme scenarios.This paper further deals with the question of extreme cases. It examines how experts should build a set of two to four well contrasted and precisely described futures that summarizes in a simple way their knowledge. Like scenario makers, these experts face multiple objectives: they have to anchor their analysis in credible expertise; depict though-provoking possible futures; but not so provocative as to be dismissed out-of-hand. The first objective can be achieved by describing a future of possibility level 1. The second and third objective, however, balance each other. We find that a satisfying balance can be achieved by selecting extreme cases that do not rule out equiprobability. For example, if there are three cases, the possibility level of extremes should be about 1/3.Futures, futurible, scenarios, possibility, imprecise probabilities, uncertainty, fuzzy logic

Pricing European stock options using stochastic and fuzzy continuous time processes

Over the past 40 years, much of mathematical finance has been built on the premise that stocks tend to move according to continuous-time stochastic processes, particularly geometric Brownian Motion. However, fuzzy set theory has recently been shown to hold promise as a model for financial uncertainty as well, with continuous time fuzzy processes used in place of Brownian Motion. And, like Brownian Motion, fuzzy processes also cannot be measured using a traditional Lebesque integral. This problem was solved on the stochastic side with the development of Ito's calculus. Likewise, the Liu integral has been developed to measure fuzzy processes. In this paper I will describe and compare the theoretical underpinnings of these models, as well as "back-test" several variations of them on historical market data

Cross-Entropy of Uncertain Variables

In order to deal with the divergence of uncertain variables from a prior one, this paper is devoted to introduce the concept of cross-entropy for uncertain variables and study the minimum cross-entropy principle