Nonlinear differential equations based on the B-S-M model in the pricing of derivatives in financial markets

The pricing and hedging of financial derivatives have become one of the hot research issues in mathematical finance today. In the case of non-risk neutrality, this article uses the martingale method and probability measurement method to study the pricing method and hedging strategy of financial derivatives. This paper also further studies the hedging strategy of financial derivatives in the incomplete market based on the BSM model and converts the solution of this problem into solving a vector on the Hilbert space to its closure. The problem of space projection is to use projection theory to decompose financial derivatives under a given martingale measure. In the imperfect market, the vertical projection theory is used to obtain the approximate pricing method and hedging strategy of financial derivatives in which the underlying asset follows the martingale process; the projection theory is further expanded, and the pricing problem of financial derivatives under the mixed-asset portfolio is obtained. Approximate pricing of financial derivatives; in the discrete state, the hedging investment strategy of financial derivatives H in the imperfect market is found through the method of variance approximation.

Grade 12 Learners’ Perceptions of Opportunities to Learn Imperfect Market Structures: Frances Baard District

This empirical study sought to investigate the grade 12 economics learners’ perceptions of opportunities to learn imperfect market structures in selected schools in the Francis Baard District of Northern Cape. A quantitative research approach was employed, where a questionnaire was administered to 253 Grade 12 economics learners from three schools in Galeshewe. The questionnaire was based on four Opportunities to Learn (OTL) variables; content exposure, content emphasis, quality of instruction, and instructional resources. Data were analysed through excel 365 and then through SPSS. Overall, the study showed that little or no opportunities to learn were being created for learners to master the concept of imperfect market structures. This study is significant because it helps to make known to both the learners and teachers, the factors influencing learners’ learning outcomes related to imperfect market structures. Learners must also be encouraged to exhibit a positive attitude towards the subject, while the economics teachers should put in the required effort to improve the learning outcomes in schools.

Growth and Residential Distribution with Solow, Alonso, and Dixit-Stiglitz Integrated

The purpose of this study is to deal with dynamic interdependence between economic growth, economic structure, and residential distribution. It develops a spatial dynamic economic model on basis of microeconomic foundation. It integrates the economic mechanisms of the Solow one-sector growth model, the Alonso spatial residential model, and the Dixit-Stiglitz equilibrium model with imperfect market. We apply neoclassical economic growth of perfect competition to describe the growth determinant, the neoclassical urban residential model to determine residential location, and the basic model of new growth theory with imperfect market to take account of perfect and imperfect competition in spatial equilibrium structure. The basic economic mechanisms of the three approaches are integrated by using Zhang new approach to formally model household behavior. We determine the motion by simulation. Then we conduct comparative dynamic analysis to analyze how exogenous changes in different parameters affect residential distribution, economic growth, and economic structure. The study shows how changes in preferences and technologies affect economic growth, economic structure, land rent, and residential distribution.

Magical banking capital: Neo-endogenous money (NEM)

This research emerges with internal financial constraint. How financial constraint may lead to economic recess or back. This financial constraint is different than external finance constraint, and is not due to lack of gold, etc. It explains the positive relationship between excess return in stock market (ERSM) and non-real funding or riskier credit. The matter comes under imperfect market banking. It includes subsequently banking behavior and failure of central bank policy to control individual banks under these circumstances. In addition, it presents measures to get awareness before default comes, as financial default rare and crisis in financial market comes much before that.

PRINCIPAL-AGENT PREFERENCES IN IMPERFECT MARKET: THEORETICAL ANALYSIS ON MURABAHAH AND IJARAH

This paper aims to determine the optimal contract for the principal and the agentin imperfect market, when murabahah and ijarah are used. The financial contractingenforceability approach is employed to determine the contract that maximizes thevalue of the firm subject to agents’ constraints when the shock is low and high, andregarding market frictions. Furthermore, this approach allows us to assess the level ofmarket frictions that agents may bear in case of low shock and high shocks. Findingsreveal that the simulated values of the market frictions’ parameters for both contractsincrease when moving from the low shock to the high shock. Such evidence impliesthat the agent is more likely to cheat and hide significant information about the projectwhen the shock is high. As a response to this higher risk, the simulated values of theprofit margin parameters for the principal rise also when the shock is high in orderto compensate for the increase of market frictions and mitigate conflicts of interest.By comparing both contracts based on the simulated optimal values of the firm, it isnoticeable that the gap between both contracts is very tight, which can be attributedto their common debt-based financial arrangements. However, the results show thatijarah allows the principal and the agent to generate the highest value in case of lowshock and high shock, comparing to murabahah. Therefore, ijarah seems to be moreattractive for the principal and the agent than murabahah.