ESI 6353 Risk & Decision Analysis

Objective: Build foundations for analytics of decision making under uncertainty and risk.

Text: Decisions with multiple objectives, R. Keeney et al., 1993.

Topics

I. Review of probability theory
(elements of set theory; events & probability spaces; Bayesian concepts; statistical independence; random variables, vectors, & functions; conditional probability & expectation; distributions & transformations)

II. Decision making under strict uncertainty
(dominated actions; decision criteria: Wald's maximin, Savage's minimax regret, Hurwicz alpha index, Laplace's principle of insufficient reasoning; mixed strategies; properties of decision criteria)

III. Decision making under risk
(Expected monetary value (EMV); decision flow diagrams; expected value of sample information (EVSI); expected opportunity loss; expected value of perfect information (EVPI); prior expectation of posterior EVPI)

IV. Unidimensional utility theory (UT). Risk attitudes
(Binary relations and preference orderings; risk profiles; stochastic dominance of reward distributions; concept of utility; response functions; transformation of state distributions; utility functions: properties and assessment; certainty equivalence & risk premium; risk attitudes; risk aversion & risk tolerance; underlying axioms of UT; common families of utility functions; decreasigly/increasingly/constant risk averse utility functions)

V. Multiattribute utility theory
(Utility independence; additive independence & additive utility functions; multiplicative & multilinear utility functions)