Quick solutions for general best choice problems in continuous time

• Published in: Communications in statistics. Stochastic models Vol. 14; no. 1-2; pp. 241 - 264
• Main Author: Thomas Bruss, F.
• Format: Journal Article
• Language: English
• Published: Monticello, NY Marcel Dekker, Inc 01.01.1998; Dekker
• Subjects: "thinning paradox"; AMS subject classification 60G40; Exact sciences and technology; exponential convergence; Mathematics; modeling dependence; monotonicity; no-information-case; Pascal process; Poisson record process; Probability and statistics; Probability theory and stochastic processes; random availability; random freeze; random number of options; Sciences and techniques of general use; Secretary problem; Stochastic processes; thinning; time dependent penalties; time scale transformation; truncation; Choice; Secretary problem; Continuous time; Random processes; Poisson process; Convergence; Random number
• ISSN: 0882-0287
• DOI: 10.1080/15326349808807469

This article introduces a multi-purpose model to tackle best choice problems in different contexts. The model allows for a random number of options (items on which a decision has to be made), random freeze times (options may be withheld after some random time), random availability of options, and recall on options. Payoff functions allow for penalties for taking no decision, or for making a wrong choice. The emphasis of our new model is on trying to reach applicability to real world situations. We provide general formulae for optimal solutions or good approximations. A large example section is provided to show the tractability and insensitivity of solutions, and, in particular, the speed at which we can obtain them