Date of Submission


Date of Award


Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name

Quantitative Economics


Theoretical Statistics and Mathematics Unit (TSMU-Kolkata)


Krishnaji, N.

Abstract (Summary of the Work)

Produotion assets which deteriorate in performance with time (or age) are required to be replaced. In general, a stream of benefits and costa are associated with every productive asset, be it a machine or a tree. Ugually, in replacement theory, the benefits and costs are taken as given functions of the age of the asset. These functions provide the oriteria for identifying the płysical condition of the asset. In simple replacement models, an asset is replaced by an ider tical one. The objective of a replacement policy is to find a sequence of time pointe (or alternatively, replacement ages) for replacing successive pieces of the asset that maximises some given objective function based on the stream of benefits and costs over the time- horizon of the invectment process. Discounted net returns, average cost over the inves tment period etc., are the most common type of objective func tions used in the literature.1.1.2 A considerable literature exists on the optimal replacement of assets in the deterministio case. This is a situation where the return from an asset at a giveni point of time is aasumed to be nor-random a given function of time or age of the asset. The objective of these tudies was to provide an understanding of the various prinoiples of asset replacement. One of the questione asked is : How is the replace ment date related to the arnuity formed by the sum of the discounted annual earnings and other such eoonomio variables ?, Most of these studies consider a atatio situaton where a piece of an asset is replaced by an identical one over an infinite horizon. See for example, Preinreich (1940), Perin (1972) , Etherington (1977)gives a brief biblio- grapty of studies on the economies of replacement. Dean (1961) has summarised various deterministic replacement models devel oped by diffe rent authors for application to industrial problems. In this study also we shall consider a static situation but our focus will be on the analy- tical characteristics of the replacement age i.e., how the replacement ago is related to the parametere that apecify the performance of the asset over time etoi We shell further attempt a comparison between the solutions corresponding to the finite- and infinite horizon cases.1.1.3 Studies which include stochastic eldments in the replac ement models have generally concentrated on unintentional replacament. Here the concern was with an asset that dies unexpeotedly. See for example Burt (1965), Jorgenson (1967). A light bulb is a typical example of this situation. The performance of this asset is stable over time but it ceases to perform all of a sudden. Thus, it life is stochastic in nature. But it is quite raro to find a replac ement study in the othor kind of stochastic situation where thero is no suddon death; of the asset but it produces benofits of stochastic nature and doteriorates over time.


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