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