The following two articles provide mathematical and statistical background on the search test stop model.
The paper by Marcozzi presents approximations of the optimal stopping problem and their solutions. In contrast, Freeman elaborates on the optimal stopping problem and its extensions, starting with the standard problem and presenting extension, considering
- full and partial information
- recall (legalizing the use of dropped choices)
- use of ranking and utility functions
[freeman1983] Freeman, P. R. (1983). ''The Secretary Problem and Its Extensions: A Review'', International Statistical Review, International Statistical Institute (ISI), pages 189--206, 51(2) [marcozzi2008] Marcozzi, Michael D. (2008). ''On the Approximation of Infinite Dimensional Optimal Stopping Problems with Application to Mathematical Finance'', Journal of Scientific Computing, Plenum Press, pages 287--307, 34(3)