Innite Horizon Optimal Search Problem with Hiring and Firing Options
Mingxin Xu · 2009
As in the classic ‘Secretary Problem’: the candidates arrive sequentially. In this paper, they are represented with i.i.d. It^ o diusion processes. Two interwoven sequences of optimal stopping times are decided which signify the hiring and ring times of each candidate. The goal is to choose the stopping times to maximize expected sum of benet and cost when the time horizon is innite. The optimality conditions in terms of Verication Theorem, Least Superharmonic Majorant, and Variational Inequalities are given. The solution for the simple Brownian case with linear cost/benet functions is calculated which results in a new two-one threshold strategy giving rise to the corresponding decisions of hiring/letting go-ring.