Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)

Legacy Department

Mathematical Science


Reneke, James A

Committee Member

Wiecek , Margaret M

Committee Member

Saltzman , Matthew J

Committee Member

Cox , Christopher L

Committee Member

Brannan , James R


Decision making has became increasingly complex as risky decisions are made in uncertain environments. To minimize risk, the problem of quantifying risk becomes very significant. In our review of the literature, we found a number of different risk measures. A closer study reveals that most of these risk measures define both risk and uncertainty in many different ways.
In this dissertation, we model uncertainty and risk based on the Knightian definition of uncertainty and risk. We propose this alternative modeling paradigm and introduce our decision making methodology by solving an illustrative problem presented by a group of decision makers from Sandia Laboratories.
Multicriteria decision problems for complex systems with interacting components require the algebra of operator representations and the separability of these representations to include the feedback due to the interacting uncertainties. However, the sum of these separable representations need not be separable. We propose a separable approximation for the sum and bound the errors due to the approximation.
The issue of consistency of our decision making methodology is also studied by resolving the Ellsberg Paradox where Ellsberg claims that good decision makers should violate Savage's axioms at times. We show that our methodology provides consistent decisions without violating Savage's axioms. This consistency of our methodology is attributed to handling the multiple criteria without aggregation.
Due to this concept of de-aggregated multiple criteria, we believe that the conventional portfolio selection problems may mislead the decision maker by confounding the criteria. We propose an alternate portfolio selection procedure from a given feasible set of portfolios. Real data for Real Estate Investment Trusts, traded in NYSE, was used to create a consistent portfolio. In this dissertation, only the initial work for this portfolio selection problem is presented. Finally, we discuss the directions for future research.