Centre for Discrete and Applicable Mathematics

 CDAM Research Report, LSE-CDAM-2000-16

August 2000

Endogenous Irreversibility With Finite Horizon Investment When Resale Is Possible

Miles B. Gietzmann and Adam J. Ostaszewski


In this paper we consider the situation where partial reversals from a finite horizon investment are possible at discrete decision times. We are able to identify a range of circumstances in which reversal is triggered by the investment resale rate,  R,  falling below a critical value  R#,  assuming  R  to be a random variable identically and independently distributed over decision times. This result is similar in qualitative form to results derived in related infinite horizon formulations in that, once the random variable hits a key ``favorable'' interval, the optimal policy switches to reversal of investment. However, we also show that the alternative geometric Brownian model for the resale rate (for  R - 1)  implies restrictions on the ranges over which reversal remains optimal which are significantly different in a number of ways. For instance we identify near-termination effects which do not arise in infinite horizon settings in which the favorable interval changes in magnitude as the final decision epoch approaches. Also we show that the optimal policy space is richer in that the range over which reversal is optimal can take a wider set of forms and so knowledge of a single  R#  may be insufficient to guide optimal investment policy. In particular we show that for certain values of the parameters a twin switching policy may be optimal under which as  R  increases, reversal is first non optimal, then optimal and finally non optimal again.

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