OPTIMAL MULTIVARIATE STOPPING RULES

@article{Assaf1998OPTIMALMS,
  title={OPTIMAL MULTIVARIATE STOPPING RULES},
  author={David Assaf and Ester Samuel-Cahn},
  journal={Journal of Applied Probability},
  year={1998},
  volume={35},
  pages={693-706}
}
symmetry assumptions we show that the optimal rule is one which (also) maximizes EZt where Zi = 1:=I Xj(i), and hence has a particularly simple structure. Examples are included, and the results are extended both to the infinite horizon case and to the case when X(1), ..., X(n) are dependent. Asymptotic comparisons between the present problem of finding sup h(EX(t)) and the 'classical' problem of finding sup Eh(X(t)) are given. Comparisons between the optimal return to the statistician and to a… 
View via Publisher
ratio.huji.ac.il
11 Citations
Highly Influential Citations
3
Background Citations
6
Methods Citations
3
Results Citations
1

11 Citations

Citation Type

Citation Type

Cooperative Stopping Rules in Multivariate Problems
Abstract Consider a sequence of random vectors Y(1),…, Y(n) in ℛ d , with a known joint distribution, finite expectations, adapted to a filtration ℱ. For a given monotone function h : ℛ d → ℛ, a…
Optimal sequential selection of a gambler assessed by the prophet
Reviewing rst connections to the literature then in chapter 2 for a nite number of stochastically independent o ers a payo function is considered, depending on the chosen value XS and on the overall…
Optimal cooperative stopping rules for maximization of the product of the expected stopped values
A best-choice problem with multiple selectors
  • H. Glickman
  • Mathematics
    Journal of Applied Probability
  • 2000
Consider a situation where a known number, n, of objects appear sequentially in a random order. At each stage, the present object is presented to d ≥ 2 different selectors, who must jointly decide…
Stopped Markov decision processes with multiple constraints
TLDR
The idea of occupation measures and using the scalarization technique for vector maximization problems is applied and the existence of a Pareto optimal pair of stationary policy and stopping time requiring randomization in at most k states is shown.
Equivalence between Random Stopping Times in Continuous Time
AbstractTwo concepts of random stopping times in continuous time have been de-fined in the literature, mixed stopping times and randomized stopping times.We show that under weak conditions these two…
Sequential correlated equilibrium in stopping games
In many situations, such as trade in stock exchanges, agents have many opportunities to act within a short interval of time. The agents in such situations can often coordinate their actions in…
Baxter-Chacon topology and optimality for multivariate multiple stopping problems
Abstract This paper is concerned with optimal stopping problems for discrete time stochastic processes with the multiple stopping rules, which are also called multivariate stopping problems or…
Sequential Correlated Equilibria in Stopping Games
TLDR
This paper presents a new solution concept for infinite-horizon dynamic games, which is appropriate for such situations: a sequential normal-form correlated approximate equilibrium, and shows that every such game admits this kind of equilibrium.
Optimal Stopping Problem with a Vector-Valued Reward Function
In this note, using the well-known method of scalarization, we give an explicit characterization of the Pareto optimal stopping time for a vector-valued optimal stopping problem with only two reward…
...
1
2
...

References

SHOWING 1-10 OF 10 REFERENCES
MULTI-VARIATE STOPPING PROBLEMS WITH A MONOTONE RULE
A monotone rule is introduced to sum up individual declarations in a multi-variate stopping problem. The rule is defined by a monotone logical function and is equivalent to the winning class of…
Optimal cooperative stopping rules for maximization of the product of the expected stopped values
Ratio comparisons of supremum and stop rule expectations
SummarySuppose X1,X2,...,Xn are independent non-negative random variables with finite positive expectations. Let Tndenote the stop rules for X1,...,Xn. The main result of this paper is that…
On the value of information in multi-agent decision theory
Testing Statistical Hypotheses
The General Decision Problem.- The Probability Background.- Uniformly Most Powerful Tests.- Unbiasedness: Theory and First Applications.- Unbiasedness: Applications to Normal Distributions.-…
Inequalities: Theory of Majorization and Its Applications
Although they play a fundamental role in nearly all branches of mathematics, inequalities are usually obtained by ad hoc methods rather than as consequences of some underlying "theory of…
A Survey of Prophet Inequalities in Optimal Stopping Theory
This paper surveys the origin and development of what has come to be known as "prophet inequalities" in optimal stopping theory. Included is a review of all published work to date on these problems,…
Monotone stopping games
Etude de l'extension des problemes d'arret optimal a des jeux strategiques a somme non nulle appeles jeux d'arret
The Asymptotic Behavior of the Reward Sequence in the Optimal Stopping of I.I.D. Random Variables
Multivariate stopping problems with a monotone rule. J
  • 1982