The Best-or-Worst and the Postdoc problems

Bayón, L.; Ayuso, Pedro Fortuny; Grau, J. M.; Oller-Marcén, Antonio M.; Ruiz, M. M.

doi:10.1007/s10878-017-0203-4

Cited by 16 publications

(18 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…If ( ) ∼ ℳ( ) then lim ( ( )) = ( ).Proof. The proof is straightforward and analogous to that presented in[3] for functions of a real variable and domain [0, ] and ( ) = ( ).…”

mentioning

confidence: 80%

An Optimal Stopping Problem for an Investing Firm

Arnau¹,

Ayuso²,

Grau³

et al. 2020

ECECSR

View full text Add to dashboard Cite

The information on the costs, benefits and opportunities is an essential tool for the study of real options in firms that make large investments.We study investment decisions regarding disruptive economies. The real options logic is unsuitable for single-investment events, which are becoming frequent in this type of economies. We propose a strategy for a firm seeking to invest in the very best technology among a sequence of opportunities. If the choice is not the best, the invested capital will be lost. The yield will depend on whether the chosen option is the best and on the investment. Our analysis shows that the optimal strategy for the investing firm is to invest a specific capital in the relatively best option after a threshold which depends on the number of opportunities.

show abstract

“…If ( ) ∼ ℳ( ) then lim ( ( )) = ( ).Proof. The proof is straightforward and analogous to that presented in[3] for functions of a real variable and domain [0, ] and ( ) = ( ).…”

mentioning

confidence: 80%

An Optimal Stopping Problem for an Investing Firm

Arnau¹,

Ayuso²,

Grau³

et al. 2020

ECECSR

View full text Add to dashboard Cite

show abstract

“…This is exemplified in a study of planning medical treatments (Bruss [15]) where a convincing way to comply with ethical constraints is to pursue a last success. Additional flexibility can also be obtained to some extent by adapting the notion of a last success to more than one selection, by focussing on the best-or-second best, as in Ano and Ando [16], Ano et al [17], and Bayón et al [18], looking at multiple stopping versions as in Tamaki [19] and Kurushima and Ano [20], and also by allowing for missing observations, as in the work of Ramsey [21].…”

Section: Last Success Problemsmentioning

confidence: 99%

Combined Games with Randomly Delayed Beginnings

Bruss

2021

Mathematics

View full text Add to dashboard Cite

This paper presents two-person games involving optimal stopping. As far as we are aware, the type of problems we study are new. We confine our interest to such games in discrete time. Two players are to chose, with randomised choice-priority, between two games G1 and G2. Each game consists of two parts with well-defined targets. Each part consists of a sequence of random variables which determines when the decisive part of the game will begin. In each game, the horizon is bounded, and if the two parts are not finished within the horizon, the game is lost by definition. Otherwise the decisive part begins, on which each player is entitled to apply their or her strategy to reach the second target. If only one player achieves the two targets, this player is the winner. If both win or both lose, the outcome is seen as “deuce”. We motivate the interest of such problems in the context of real-world problems. A few representative problems are solved in detail. The main objective of this article is to serve as a preliminary manual to guide through possible approaches and to discuss under which circumstances we can obtain solutions, or approximate solutions.

show abstract

“…The following theorem (see [2,Section 4]) establishes the relation between the optimal strategies in the Best-or-Worst problem and the Postdoc problem when the number of objects in known. Theorem 1.…”

Section: The Relation Between the Best-or-worst Problem And The Postdmentioning

confidence: 99%