A continuous-time search model with finite horizon

Abstract

A variant of the continuous-time search model of Zuckerman is studied. A fixed number of identical items are for sale over a finite time horizon. Offers of i.i.d. random sizes arrive at time instances forming a renewal process; every time the salesman decides to wait for a new offer ,a fixed amount has to be paid. Search with or without recall is considered. We derive optimal strategies (maximizing the expected gain) for both cases. In the situation with recall the optimal strategy is seen to be in the form `'sell all if the maximum offer so far is greater than or equal to some threshold value'', which is a non-decreasing function of the remaining selling-time. This function is given explicitly. In the case without recall the optimal strategy is of a similar, but more complicated form.