Measurable Multiattribute Value Functions for Portfolio Decision Analysis

Abstract

Portfolio decision analysis models support selecting a portfolio of projects in view of multiple objectives and limited resources. These models often rely on the additive-linear portfolio value function, although empirical evidence suggests that the underlying preference assumptions do not always hold. In this paper we relax these assumptions and derive a more general class of portfolio value functions which deploy symmetric multilinear functions to capture non-linearities in the criterion specific portfolio values. These criterion specific portfolio values can be aggregated with an additive, a multiplicative or a multilinear function allowing a rich representation of preferences among the multiple objectives. We develop novel techniques for eliciting these value functions and also discuss the use of existing techniques that are often applied in practice.Furthermore, we demonstrate that the value functions can be maximized for problem sizes of practical relevance using an implicit enumeration algorithm or an approximate mixed integer linear programming model. Application of the results is illustrated with an example in ecological conservation site selection.

Optimization of multiple satisfaction levels in portfolio decision analysis

“…In this way, efficient portfolios and associated weights can be identified simultaneously. Finally, [46] developed a more general class of portfolio value functions which deploy symmetric multi-linear functions to capture nonlinearities in the criterion specific portfolio values. These per-criterion portfolio values can be aggregated with some additive, multiplicative or multi-linear functions allowing a rich representation of preferences.…”

Multiple Criteria Decision Analysis

“…We now impose another condition on preferences (see [14] and [15] for a use of this principle). To do this, we have to de…ne an indi¤erence relation:…”

“…A surprising feature of the literature is that other than [12] and [14], essentially no authors seem to have taken on the task of axiomatising MCPDA models speci…cally. Thus, while the normative theory underpinning multicriteria single choice has grown enormously since the early 1980s, the normative theory of MCPDA has been essentially stagnant.…”

Portfolio optimization of safety measures for reducing risks in nuclear systems

“…For identifying the optimal portfolio of safety measures, we have developed the implicit enumeration algorithm in Appendix, based on Liesiö [26]. While the algorithm is computationally viable, its computational time depends on the number of nodes of the BBN and the amount of alternative safety measures per node.…”