Optimal Stopping Problem with a Vector-Valued Reward Function

2014 ◽  
Vol 35 (6) ◽  
pp. 777-781
Author(s):  
Cloud Makasu
Keyword(s):  
Optimal Stopping ◽  
Optimal Stopping Problem ◽  
Reward Function ◽  
Vector Valued

An Optimal Stopping Problem Arising from a Decision Model with Many Agents

1998 ◽  
Vol 12 (3) ◽  
pp. 393-408 ◽  
Author(s):  
Bruno Bassan ◽  
Claudia Ceci
Keyword(s):  
Markov Process ◽  
Stefan Problem ◽  
Optimal Stopping ◽  
Economic Model ◽  
Decision Model ◽  
Value Function ◽  
Lower Semicontinuous ◽  
Social Planner ◽  
Optimal Stopping Problem ◽  
Reward Function

We study an optimal stopping problem for a nonhomogeneous Markov process, with a reward function that is lower semicontinuous everywhere and smooth in certain regions. We prove that the payoff (value function) is lower semicontinuous as well and solves a so-called generalized Stefan problem in each of these regions. We provide some results for the geometry of the “stopping observations” set. Our results generalize those in Bassan, Brezzi, and Scarsini (1996). The problem we consider stems from an economic model in which several self-interested agents desire information, whereas a social planner, although benevolent toward the agents, might decide to withhold information in order to induce diversification in their behavior.

scholarly journals On a simple optimal stopping problem

1973 ◽  
Vol 5 (4) ◽  
pp. 297-312 ◽  
Author(s):  
William M. Boyce
Keyword(s):  
Optimal Stopping ◽  
Optimal Stopping Problem

A Note on a Lower Bound for the Multiplicative Odds Theorem of Optimal Stopping

2014 ◽  
Vol 51 (03) ◽  
pp. 885-889 ◽  
Author(s):  
Tomomi Matsui ◽  
Katsunori Ano
Keyword(s):  
Lower Bound ◽  
Optimal Stopping ◽  
Secretary Problem ◽  
Bernoulli Trials ◽  
Optimal Stopping Problem ◽  
Maximum Probability ◽  
Optimal Stopping Rule ◽  
Optimal Probability ◽  
Optimal Stopping Theory ◽  
Special Case

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.

The Optimal Stopping Problem

1969 ◽  
pp. 87-145
Author(s):  
Evgenii B. Dynkin ◽  
Aleksandr A. Yushkevich
Keyword(s):  
Optimal Stopping ◽  
Optimal Stopping Problem
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