2019/04/05 by Hugh Entwistle, Entwistle, Hugh, Christopher J. Lustri +3 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Health Professions · #62L15 #Auction Theory and Applications #FOS: Mathematics #Healthcare Operations and Scheduling Optimization #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1904.02875
openalex publication_date 2019/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider optimal stopping problems, in which a sequence of independent random variables is drawn from a known continuous density. The objective of such problems is to find a procedure which maximizes the expected reward; this is often known as the "full information" problem. In this analysis, we obtain asymptotic expressions for the expectation and variance of the optimal stopping time as the number of drawn variables becomes large. In the case of distributions with infinite upper bound, the asymptotic behaviour of these statistics depends solely on the algebraic power of the probability distribution decay rate in the upper limit. In the case of densities with finite upper bound, the asymptotic behaviour these statistics depend on the algebraic form of the distribution near the finite upper bound. Explicit calculations are provided for several common probability density functions, which are compared to numerical simulations that support the asymptotic predictions.