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Utility transversality: a value‐based approach
Author(s) -
Matheson James E.,
Abbas Ali E.
Publication year - 2005
Publication title -
journal of multi‐criteria decision analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.462
H-Index - 47
eISSN - 1099-1360
pISSN - 1057-9214
DOI - 10.1002/mcda.395
Subject(s) - transversality , expected utility hypothesis , preference relation , subjective expected utility , value (mathematics) , function (biology) , bellman equation , preference , mathematical economics , risk aversion (psychology) , relation (database) , multilinear map , von neumann–morgenstern utility theorem , dimension (graph theory) , decision theory , mathematics , economics , computer science , microeconomics , mathematical analysis , statistics , database , evolutionary biology , pure mathematics , biology
We examine multiattribute decision problems where a value function is specified over the attributes of a decision problem, as is typically done in the deterministic phase of a decision analysis. When uncertainty is present, a utility function is assigned over the value function to represent the decision maker's risk attitude towards value, which we refer to as a value‐based approach. A fundamental result of using the value‐based approach is a closed form expression that relates the risk aversion functions of the individual attributes to the trade‐off functions between them. We call this relation utility transversality. The utility transversality relation asserts that once the value function is specified there is only one dimension of risk attitude in multiattribute decision problems. The construction of multiattribute utility functions using the value‐based approach provides the flexibility to model more general functional forms that do not require assumptions of utility independence. For example, we derive a new family of multiattribute utility functions that describes richer preference structures than the usual multilinear family. We also show that many classical results of utility theory, such as risk sharing and the notion of a corporate risk tolerance, can be derived simply from the utility transversality relations by appropriate choice of the value function. Copyright © 2007 John Wiley & Sons, Ltd.