A new continuous-time search model

The paper studies a search model in which offers of random size are received randomly over time. The arrival times form a point process of a certain type, and the offer size distribution may depend on the corresponding arrival time. The search costs have a time-dependent cost rate. The objective is to stop the search process such that the expected discounted net reward (associated with the maximum offer received so far) is maximized. A stopping time σ is suggested, and conditions are specified under which σ turns out to be optimal.