Some problems in decision making associated with random walks
type: Item
instance of: scholarly article
title: Some problems in decision making associated with random walks
zbMATH Open document ID: 0915.90252
author: N. N. Evtikhiev
author: Aleksandr A. Vasin
published in: Moscow University Computational Mathematics and Cybernetics
publication date: 1999-04-14T00:00:00Z
review text: Problems of the decision making theory related to the motion of a point or an object on an integer lattice are generally connected with an analysis of asymptotics of the probability distribution of finding the point in the knots of the lattice. The asymptotics are considered for a case when the time of the motion tends to infinity. The analysis of a motion control and a design of the optimal control strategy are presented in the article. It is supposed that a transfer probability in relation to one of the coordinates defined by an operating side while transfer probabilities in relation to other coordinates are noncontrollable factors. Additionally it is supposed that in the knots of the lattice a gain function is given. Using different assumptions some optimal strategies of the operating side are defined. The following situations are considered: 1) choice of the transfer probability in relation to the first coordinate comes true when the value of the noncontrollable factor is known; 2) as to transfers in relation to the second coordinate it is known only its possible values in the next period. The optimal critaria are: a) mean value of the gain; b) the maximal value of the gain which can be guaranteed with a given confidence probability; c) the probability of getting of a gain not less that the given one . The research is presented for two classes of the gain function which are especially interesting for auctions of shares etc.
Mathematics Subject Classification ID: 90C40
Mathematics Subject Classification ID: 91B26
Mathematics Subject Classification ID: 91B06
zbMATH DE Number: 1276089
zbMATH Keywords: decision theory
zbMATH Keywords: random walk
zbMATH Keywords: optimal control strategy
zbMATH Keywords: auctions of shares
MaRDI profile type: Publication
Recommended article: Q4351266
Recommended article: Some problems concerning the structure of random walk paths
Recommended article: Q3766608
Recommended article: Choice and Bias in Random Walks
Recommended article: Q4512062
Recommended article: A Generalization of a Random Walk Problem
Recommended article: Q3706277
Recommended article: Q4863397
Recommended article: Q5807214
Recommended article: Q4641989
description: scientific article; zbMATH DE number 1276089