Abstract
This paper analyzes the determinants of asset replacement investment decisionswith maintenance and operating cost uncertainty governed by a mixed modifiedfractional Brownian motion. It addresses an important issue in investment decision-making and offers an innovative approach using mixed modified fractional Brownianmotion. The contingent claims method from the real options literature providingtechniques needed to incorporate uncertainty into replacement investment decisions.Following Mauer et Ott [4], we note that the optimal time of replacement of thefixed assets in a firm depends on the policy of optimal replacement which is a criticallevel of the costs of maintenance and exploitation. The optimal replacement policy isobtained as a function of the present average value of the maintenance and operatingcosts of the assets. By assuming that the cost of operating and maintenance assetsfollow a Mixed Modified Fractional Brownian Motion (MMFBM) [6], the optimalreplacement policy is minimal and therefore it encourages the firm to replace more ofits assets and spend less their maintenance, depending on the MMFBM parameterssuch as Hurst coefficient. At the end we notice that when the Hurst parameterincreases, the optimal replacement policy and the maximum value of the presentaverage value function of asset costs decrease.