An optimal search for a disappearing target with a random lifetime

The authors consider an optimal search for a disappearing target with a random lifetime. A stationary target hides in some boxes at the beginning of the search and disappears at some time which is a random variable. A searcher cannot detect the target after it disappears. The searcher is given some reward by the detection of the target by having permission to use some searching effort with cost for the detection. This paper deals with an optimal distribution of searching effort and an optimal stopping time minimizing the expected risk (the expected cost minus the expected reward) and the conditions of the optimality are obtained. Numerical examples are examined and the relations between this paper and previous studies are also discussed.