A persistency problem connected with a point process

Imagine a man owning a commodity, e.g., a house, which is for sale. Offers at varying amounts are coming in every now and then. The longer he postpones selling the more he loses because of deterioration, interest losses, or the like. At each offer he must decide whether to accept it or wait for a better one. (A more picturesque example would be that of a girl scrutinizing successive suitors.)