The research objective of this award is to study concepts of relaxed univariate and multivariate stochastic dominance motivated from the specification of utility functions. A major challenge in risk-adjusted decision making is the assessment of a decision maker's risk/utility function associated with uncertain outcomes. The stochastic dominance concept enables the defining of preferences of one random entity (variable, vector, matrix, process, etc.) over another and therefore can be used to compare the different risks between decision alternatives. The concept of stochastic dominance is related to utility theory, which works with a class of utility functions where limited prior knowledge on a decision maker's utility function is assumed, which unfortunately results in very conservative models. Developing models, and the corresponding algorithms, that can systematically circumvent the challenges of traditional utility theory, especially when the decision is based on conflicting objectives and multiple random outcomes, is thus critically needed.
If successful, the results of this research will lead to the development of a new class of risk-adjusted decision models that incorporate risk in a more realistic way than currently existing techniques. Computationally efficient algorithms will be developed to solve these models.