Harmonised Fractal dimensional Measure: A Special Case of a Haar Measure and Convenience With Martingales

Abstract

The Martingale's property is one of the fundamental mathematical properties which underline many important results in finance, obeying the principle of risk neutral pricing and a necessary condition for an efficient market. The aim of this paper is to show that the Harmonized fractal dimensional measure (HFDM) is a special case of a Haar measure and also convenience with martingale measure. To establish this, we first transform the measure into a solution then checkmate it under the Martingale properties. In this sense, the efficiency of harmonized fractal dimensional measure in capital market connotes that the measure is a martingale as it deals with wealth distribution that are highly skewed, curbs investment by neutralizing risky assets and diverting the wealth to consumption.