The optimal economic lifetime of vintage capital in the presence of operating costs, technological progress, and learning

Algorithms for asset replacement under limited technological forecast

“…The technological change leads to the availability of newer assets that require less maintenance and/or are less expensive, so P(t) and A(t,u) decrease in t. The maintenance cost A(t,u) usually increases in the age uÀ t (as the asset becomes older) because of physical deterioration, however, it can also decrease because of learning (Goetz et al, 2008). The general form of the function A(t,u) can depict various hypotheses of deterioration and learning.…”

Convergence of numerical solutions for a class of stochastic age-dependent capital system with fractional Brownian motion

“…Stochastic partial differential equations have been widely used to model the phenomena arising in many fields of science and industry such as finance, economics, biology and medicine, see e.g., [4,6,12,13,19,21] and references therein. Recently, the numerical construction of stochastic agedependent (vintage) capital system with standard Brownian motion has captured many researchers' attention.…”

“…For instance, Feichtinger et al [4,5] established deterministic (vintage) capital dynamics and the necessary optimality conditions, and developed the vintage capital stock model with technological progress while the model is solved. Goetz et al [6] studied the capital replacement decision of a firm as a distributed investment and disinvestment optimal control problem.…”

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“…The quantity of defective products is a random variable and has general discrete distributions. Goetz et al (2008) generalized the transfer time of the Pavitsos and Kyriakidis (2009) model and derived the optimal cost limit.…”