The Effectiveness of Applying the Jigsaw Model in Learning Indonesian Exposition Texts for Class Viii State Junior High School 4 Sendana, Majene Regency

This study aims to describe the effectiveness of the application of the jigsaw model in learning to write Indonesian exposition texts for class VIII SMP Negeri 4 Sendana in Majene. The type of research used is a quasi-experimental type experiment with two groups, namely the control group and the experimental group who were given a pretest and posttest. These two groups aim to prove whether the jigsaw learning model is effectively used or not in class VIII of SMP Negeri 4 Sendana. Before implementing Jigsaw Model, the results of the study suggest less successful, as shown by the 17 pupils who can only answer the questions that have been presented. As demonstrated by 51 students who were able to answer questions, the outcomes of studying exposition texts using the jigsaw learning approach in class VIII were successful.

Discrete Time Hedging of the American Option

In a complete financial market we consider the discrete time hedging of the American option with a convex payoff. It is well-known that for the perfect hedging the writer of the option must trade continuously in time which is impossible in practice. In reality, the writer hedges only at some discrete time instants. The perfect hedging requires the knowledge of the partial derivative of the value function of the American option in the underlying asset, explicit form of which is unknown in most cases of practical importance. At the same time several approxima- tion methods are developed for the calculation of the value function of the American option. We establish in this thesis that, having at hand any uniform approximation of the American option value function at the equidistant discrete rebalancing times it is possible to construct a discrete time hedging portfolio the value process of which uniformly approximates the value process of the continuous time perfect delta-hedging portfolio. We are able to estimate the corresponding discrete time hedging error that leads to complete justification of our hedging method for the non-increasing convex payoff functions including the important case of the American put. It is essentially based on a recently found new type square integral estimate for the derivative of an arbitrary convex function by Shashiash [23]. We generalize the latter square integral estimate to the case of the family of the weight functions, satisfying certain conditions.