scholarly journals A survey of prophet inequalities in optimal stopping theory

Author(s):  
Theodore P. Hill ◽  
Robert P. Kertz
2014 ◽  
Vol 51 (03) ◽  
pp. 885-889 ◽  
Author(s):  
Tomomi Matsui ◽  
Katsunori Ano

In this note we present a bound of the optimal maximum probability for the multiplicative odds theorem of optimal stopping theory. We deal with an optimal stopping problem that 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 Bruss' (2000) odds problem. In a previous work, Tamaki (2010) derived an optimal stopping rule. We present a lower bound of the optimal probability. Interestingly, our lower bound is attained using a variation of the well-known secretary problem, which is a special case of the odds problem.


2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Xin Zheng ◽  
Yu Nan ◽  
Fangsu Wang ◽  
Ruiqing Song ◽  
Gang Zheng ◽  
...  

Considering the widespread use of mobile devices and the increased performance requirements of mobile users, shifting the complex computing and storage requirements of mobile terminals to the cloud is an effective way to solve the limitation of mobile terminals, which has led to the rapid development of mobile cloud computing. How to reduce and balance the energy consumption of mobile terminals and clouds in data transmission, as well as improve energy efficiency and user experience, is one of the problems that green cloud computing needs to solve. This paper focuses on energy optimization in the data transmission process of mobile cloud computing. Considering that the data generation rate is variable, because of the instability of the wireless connection, combined with the transmission delay requirement, a strategy based on the optimal stopping theory to minimize the average transmission energy of the unit data is proposed. By constructing a data transmission queue model with multiple applications, an admission rule that is superior to the top candidates is proposed by using secretary problem of selecting candidates with the lowest average absolute ranking. Then, it is proved that the rule has the best candidate. Finally, experimental results show that the proposed optimization strategy has lower average energy per unit of data, higher energy efficiency, and better average scheduling period.


2014 ◽  
Vol 41 (15) ◽  
pp. 6796-6806 ◽  
Author(s):  
Kostas Kolomvatsos ◽  
Christos Anagnostopoulos ◽  
Stathes Hadjiefthymiades

Author(s):  
Tomas Björk

In this chapter we present the dynamic programming approach to optimal stopping problems. We start by presenting the discrete time theory, deriving the relevant Bellman equation. We present the Snell envelope and prove the Snell Envelope Theorem. For Markovian models we explore the connection to alpha-excessive functions. The continuous time theory is presented by deriving the free boundary value problem connected to the stopping problem, and we also derive the associated system of variational inequalities. American options are discussed in some detail.


2021 ◽  
pp. 2150049
Author(s):  
Siham Bouhadou ◽  
Youssef Ouknine

In the first part of this paper, we study RBSDEs in the case where the filtration is non-quasi-left-continuous and the lower obstacle is given by a predictable process. We prove the existence and uniqueness by using some results of optimal stopping theory in the predictable setting, some tools from general theory of processes as the Mertens decomposition of predictable strong supermartingale. In the second part, we introduce an optimal stopping problem indexed by predictable stopping times with the nonlinear predictable [Formula: see text] expectation induced by an appropriate backward stochastic differential equation (BSDE). We establish some useful properties of [Formula: see text]-supremartingales. Moreover, we show the existence of an optimal predictable stopping time, and we characterize the predictable value function in terms of the first component of RBSDEs studied in the first part.


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