A short survey of normative properties of possibility distributions

In 2001 Carlsson and Full´er [1] introduced the possibilistic mean value, variance and covariance of fuzzy numbers. In 2003 Full´er and Majlender [4] introduced the notations of crisp weighted possibilistic mean value, variance and covariance of fuzzy numbers, which are consistent with the extension principle. In 2003 Carlsson, Full´er and Majlender [2] proved the possibilisticCauc hy-Schwartz inequality. Drawing heavily on [1, 2, 3, 4, 5] we will summarize some normative properties of possibility distributions

Some applications of possibilistic mean value, variance, covariance and correlation

In 2001 we introduced the notions of possibilistic mean value and variance of fuzzy numbers. In this paper we list some works that use these notions. We shall mention some application areas as wel

A Possibilistic and Probabilistic Approach to Precautionary Saving

This paper proposes two mixed models to study a consumer's optimal saving in the presence of two types of risk.Comment: Panoeconomicus, 201

Possibilistic risk aversion with many parameters

AbstractThe study of risk aversion of an agent confronted by a risk situations with several parameters is an important topic of risk theory. It is tackled traditionally with probabilistic methods. When these do not offer an appropriate shaping we can use Zadeh's possibility theory. In this paper a possibilistic model of risk aversion with several parameters is proposed. The notion of possibilistic risk premium vector is introduced as a measure of an agent's risk aversion to a situation with several risk parameters. The main result of the paper is an approximate calculation formula of this indicator. The way we can apply this model in risk aversion evaluation in grid computing is sketched out

On theoretical pricing of options with fuzzy estimators

AbstractIn this paper we present an application of a new method of constructing fuzzy estimators for the parameters of a given probability distribution function, using statistical data. This application belongs to the financial field and especially to the section of financial engineering. In financial markets there are great fluctuations, thus the element of vagueness and uncertainty is frequent. This application concerns Theoretical Pricing of Options and in particular the Black and Scholes Options Pricing formula. We make use of fuzzy estimators for the volatility of stock returns and we consider the stock price as a symmetric triangular fuzzy number. Furthermore we apply the Black and Scholes formula by using adaptive fuzzy numbers introduced by Thiagarajah et al. [K. Thiagarajah, S.S. Appadoo, A. Thavaneswaran, Option valuation model with adaptive fuzzy numbers, Computers and Mathematics with Applications 53 (2007) 831–841] for the stock price and the volatility and we replace the fuzzy volatility and the fuzzy stock price by possibilistic mean value. We refer to both cases of call and put option prices according to the Black & Scholes model and also analyze the results to Greek parameters. Finally, a numerical example is presented for both methods and a comparison is realized based on the results