On the Causal and Topological Structure of the 22-Dimensional Minkowski Space

A list of all possible causal relations in the $2$-dimensional Minkowski space $M$ is exhausted, based on the duality between timelike and spacelike in this particular case, and thirty topologies are introduced, all of them encapsulating the causal structure of $M$. Generalisations of these results are discussed, as well as their significance in a discussion on spacetime singularities

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

(Quasi)-uniformities on the set of bounded maps

From real analysis it is known that if a sequence {fn,   n∈ℕ} of real-valued functions defined and bounded on X⊂ℝ converges uniformly to f, then f is also bounded and the sequence {fn,   n∈ℕ}. In the present paper we generalize results as the above using (quasi)-uniform structures