Low Volatility Options and Numerical Diffusion of Finite Difference Schemes

2000 Mathematics Subject Classification: 65M06, 65M12.In this paper we explore the numerical diffusion introduced by two nonstandard finite difference schemes applied to the Black-Scholes partial differential equation for pricing discontinuous payoff and low volatility options. Discontinuities in the initial conditions require applying nonstandard non-oscillating finite difference schemes such as the exponentially fitted finite difference schemes suggested by D. Duffy and the Crank-Nicolson variant scheme of Milev-Tagliani. We present a short survey of these two schemes, investigate the origin of the respective artificial numerical diffusion and demonstrate how it could be diminished

Malaysian PBL Approaches: Shaping World-Class TVET Skills towards IR 4.0

An Industrial Revolution 4.0 promoted by Malaysian government entitles the rapid growth of manufacturing sector thus promotes a multi-level of workforce and skilled work force needed to satisfy the rapid technological development application. The challenges arise on preparing the individuals to meet with the current business at adequate skills level and the student need to be prepared in such way satisfied the business expectations. Looking into this situation, this paper aims to study the concept of correlation between active learning method known as Problem-Based Learning (PBL) Method and required employability skills in TVET. As an initiative to enrich the future opportunity on empowering TVET skills, this study assumes that there is positive relationship between employability skills and PBL approaches in improving student’s quality and skills. The method of study involves documentation analysis on previous research to proves the importance of employability skills in enhancing student’s competencies and the effectiveness of Problem-Based Learning Method in preparing the students to meet the expectations. The main findings of this study claimed that there was a positive relationship between employability skills and PBL learning method. Result acknowledge that PBL has the ingredients to help develop employability skills and student’s behavior. Through PBL, students learn to become more associates in the teaching and learning processes as they take responsibility throughout the learning process. It would suggest that the educational institution should emphasize the needs of the industry and students by creating awareness and guiding the students in self-analysis and in acquisition of skills

Finite Embeddability of Sets and Ultrafilters

A set A of natural numbers is finitely embeddable in another such set B if every finite subset of A has a rightward translate that is a subset of B. This notion of finite embeddability arose in combinatorial number theory, but in this paper we study it in its own right. We also study a related notion of finite embeddability of ultrafilters on the natural numbers. Among other results, we obtain connections between finite embeddability and the algebraic and topological structure of the Stone-Cech compactification of the discrete space of natural numbers. We also obtain connections with nonstandard models of arithmetic.Comment: to appear in Bulletin of the Polish Academy of Sciences, Math Serie