Related papers: The Duration of Optimal Stopping Problems
We provide a characterization of an optimal stopping time for a class of finite horizon time-inconsistent optimal stopping problems (OSPs) of mean-field type, adapted to the Brownian filtration, including those related to mean-field…
In the classical secretary problem, one attempts to find the maximum of an unknown and unlearnable distribution through sequential search. In many real-world searches, however, distributions are not entirely unknown and can be learned…
We study an optimal stopping problem under non-exponential discounting, where the state process is a multi-dimensional continuous strong Markov process. The discount function is taken to be log sub-additive, capturing decreasing impatience…
We consider a sequence of independent random variables with the known distribution observed sequentially. The observation $n$ is assumed to be a value of one order statistics such as s:n-th, where 1 is less than s is less than n. It the…
Stop-loss rules are often studied in the financial literature, but the stop-loss levels are seldom constructed systematically. In many papers, and indeed in practice as well, the level of the stops is too often set arbitrarily. Guided by…
We describe a variational approach to solving optimal stopping problems for diffusion processes, as an alternative to the traditional approach based on the solution of the free-boundary problem. We study smooth pasting conditions from a…
For three natural classes of dynamic decision problems; 1. additively separable problems, 2. discounted problems, and 3. discounted problems for a fixed discount factor; we provide necessary and sufficient conditions for one sequential…
We employ a natural method from the perspective of the optimal stopping theory to analyze entry-exit decisions with implementation delay of a project, and provide closed expressions for optimal entry decision times, optimal exit decision…
We consider a type of optimal switching problems with non-uniform execution delays and ramping. Such problems frequently occur in the operation of economical and engineering systems. We first provide a solution to the problem by applying a…
As a famous result, the ``37\% Law'' for Secretary Problem has widely influenced peoples' perception on online decision strategies about choice. However, using this strategy, too many attractive candidates may be rejected in the first 37\%,…
When facing many options, we narrow down our focus to very few of them. Although behaviors like this can be a sign of heuristics, they can actually be optimal under limited cognitive resources. Here we study the problem of how to optimally…
This study is concerned with the determination of optimal appointment times for a sequence of jobs with uncertain duration. We investigate the data-driven Appointment Scheduling Problem (ASP) when one has $n$ observations of $p$ features…
People are often reluctant to sell a house, or shares of stock, below the price at which they originally bought it. While this is generally not consistent with rational utility maximization, it does reflect two strong empirical regularities…
We study an optimal process control problem with multiple assignable causes. The process is initially in-control but is subject to random transition to one of multiple out-of-control states due to assignable causes. The objective is to find…
We consider the non-linear optimal multiple stopping problem under general conditions on the non-linear evaluation operators, which might depend on two time indices: the time of evaluation/assessment and the horizon (when the reward or loss…
The halting problem is undecidable --- but can it be solved for "most" inputs? This natural question was considered in a number of papers, in different settings. We revisit their results and show that most of them can be easily proven in a…
The hiring problem is studied for general strategies based only on the relative ranking of the candidates; this includes some well known strategies studied before such as hiring above the median. We give general limit theorems for the…
Optimising queries in real-world situations under imperfect conditions is still a problem that has not been fully solved. We consider finding the optimal order in which to execute a given set of selection operators under partial ignorance…
We consider a Bayesian persuasion or information design problem where the sender tries to persuade the receiver to take a particular action via a sequence of signals. This we model by considering multi-phase trials with different…
In this paper, we present a novel method for computing the asymptotic values of both the optimal threshold, and the probability of success in sequences of optimal stopping problems. This method, based on the resolution of a first-order…