A Note on Bruss' Stopping Problem with Random Availability
نویسندگان
چکیده
Bruss (1987) has studied a continuous-time generalization of the so-called secretary problem, where options arise according to homogeneous Poisson processes with an unknown intensity of . In this note, the solution is extended to the case with random availability, that is, there exists a xed known probability p(0 < p 1) of availability, and the number of o ering chances allowed at most is m( 1). The case when the probability of availability depends on m is also studied.
منابع مشابه
A Note on Lower Bound for Multiplicative Odds Theorem of Optimal Stopping
This note provides a bound of the optimal maximum probability for the multiplicative odds theorem in optimal stopping theory. We deal with an optimal stopping problem which maximizes the probability of stopping on any of the last m successes of a sequence of independent Bernoulli trials of length N, where m and N are predetermined integers satisfying 1 ≤ m < N . This problem is an extension of ...
متن کاملLower Bounds for Bruss' Odds Problem with Multiple Stoppings
This paper deals with Bruss’ odds problem with multiple stopping chances. A decision maker observes sequentially a sequence of independent 0/1 (failure/success) random variables with the objective to predict the last success correctly with multiple stopping chances. First, we give a nontrivial lower bound of the probability of win (obtaining the last success) for the problem with m-stoppings. N...
متن کاملThe Sum-the-Odds Theorem with Application to a Stopping Game of Sakaguchi
The optimal stopping problem of maximizing the probability of stopping on the last success of a finite sequence of independent Bernoulli trials has been studied by Hill and Krengel (1992), Hsiau and Yang (2000) and Bruss (2000). The optimal stopping rule of Bruss stops when the sum of the odds of future successes is less than one. This Sum-the-Odds Theorem is extended in several ways. First, an...
متن کاملA refined and asymptotic analysis of optimal stopping problems of Bruss and Weber
The classical secretary problem has been generalized over the years into several directions. In this paper we confine our interest to those generalizations which have to do with the more general problem of stopping on a last observation of a specific kind. We follow Dendievel [10], [11], (where a bibliography can be found) who studies several types of such problems, mainly initiated by Bruss [3...
متن کاملThe best choice problem for random number of objects with a refusal probability
In this note, wewill consider the best choice problem for random number of objects with a refusal probability. There aremany papers and books on this subject fromChow/Robbibs/Siegmund(1971), Siryaev(1973) downward. These problems has been close relations with the martingale theory, the potential theory, the optimality principle in the mathematical programming. And now it is derived the optimal ...
متن کامل