A ranking approach for robust portfolio decision analysis based on multilinear portfolio utility functions and incomplete preference information

Uncertainties are often present in typical portfolio decision analysis (PDA), and it is prudent to conduct a robust PDA to identify project portfolios that perform reasonably well across the entire range of uncertain parameter values. Previous research on robust PDA and applications has almost entirely relied on additive portfolio preference functions, with little research on robustness under multilinear portfolio utility functions (PUFs). A ranking approach for robust PDA is proposed based on multilinear PUFs, incomplete preference information, and the algorithm for accelerating stochastic multicriteria acceptability analysis (SMAA). First, the initial set of portfolios is screened through various constraints to produce a smaller set of desirable portfolios. Second, several types of incomplete preference information are thought to be elicited with regard to multilinear PUFs, including preference information on coefficients, portfolios, and uncertainties on preference elicitation techniques. Third, the SMAA decomposition algorithm is implemented as a ranking approach to perform robust PDA on the basis of multilinear PUFs, incomplete preference information, and potentially numerous portfolios in the set of desirable portfolios. Finally, the approach is applied to a case to validate its effectiveness, and comparisons among additive, multiplicative, and multilinear PUFs in terms of decision recommendations are performed.