Depreciation: A Stochastic Approach

This paper introduces a rationale for modelling physical depreciation under uncertainty and compares two variants of it. The first variant leads to a model, the 'gamma' model which has been discussed in the literature, while the second variant leads to a model, the 'binomial' model, which has not been investigated before. The binomial model is shown to approach a deterministic limit (the reducing balance method) as the depreciated asset becomes infinitely divisible. In contrast it has been demonstrated in the literature that the gamma model approaches a particular statistical distribution under these circumstances. The paper goes on to investigate the useful lives of assets under the two models, by reporting results on waiting times, none of which have appeared in the literature before.