Analysis of replacement investment decisions under maintenance and operating costs uncertainty using MMFBM

This paper analyzes the determinants of asset replacement investment decisions with maintenance and operating cost uncertainty governed by a mixed modified fractional Brownian motion. It addresses an important issue in investment decision- making and offers an innovative approach using mixed modified fractional Brownian motion. The contingent claims method from the real options literature providing techniques needed to incorporate uncertainty into replacement investment decisions. Following Mauer et Ott [4], we note that the optimal time of replacement of the fixed assets in a firm depends on the policy of optimal replacement which is a critical level of the costs of maintenance and exploitation. The optimal replacement policy is obtained as a function of the present average value of the maintenance and operating costs of the assets. By assuming that the cost of operating and maintenance assets follow a Mixed Modified Fractional Brownian Motion (MMFBM) [6], the optimal replacement policy is minimal and therefore it encourages the firm to replace more of its assets and spend less their maintenance, depending on the MMFBM parameters such as Hurst coefficient. At the end we notice that when the Hurst parameter increases, the optimal replacement policy and the maximum value of the present average value function of asset costs decrease.