Bounds on the value of information in uncertain decision problems II

Abstract

In most stochastic decision problems one has the opportunity to collect information that would partially or totally eliminate the inherent uncertainty. One wishes to compare the cost and value of such information in terms of the decision maker's preferences to determine an optimal information gathering plan. The calculation of the value of information generally involves oneor more stochastic recourse problems as well as one or more expected value distribution problems. The difficulty and costs of obtaining solutions to these problems has led to a focus on the development of upper and lower bounds on the various subproblems that yield bounds on the value of information. In this paper we discuss published and new bounds for static problems with linear and concave preference functions for partial and perfect information. We also provide numerical examples utilizing simple production and investment problems that illustrate the calculations involved in the computation of the various bounds and provide a setting for a comparison of the bounds that yields some tentative guidelines for their use. The bounds compared are the Jensen's Inequality bound,the Conditional Jensen's Inequality bound and the Generalized Jensen and Edmundson-Madansky bounds.

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