Date: Thursday, February 28, 2013
Location: 1360 East Hall (3:00 PM to 4:00 PM)
Title: Risk-averse optimization via stochastic order constraints
Abstract: Stochastic orders formalize preferences among random outcomes and are widely used in statistics and economics. We focus on stochastic optimization problems involving stochastic order relations as constraints. These constraints relate performance functionals, depending on our decisions to benchmark random outcomes shaping the risk according to the distribution of the benchmark. Necessary and sufficient conditions of optimality and duality theory for these problems will be presented. The analysis puts additional light on the expected utility theory, the dual (rank-dependent) utility theory, and the theory of coherent measures of risk. We prove that Lagrange multipliers associated with two different formulations of these constraints can be identified with utility functions, or with rank-dependent utility functions. Furthermore, we demonstrate that mean-risk models with law invariant coherent risk measures appear as Lagrangian relaxations of the problem with stochastic dominance constraints. The optimization models with stochastic order constraints provide a link between various approaches for risk-averse optimization.
The results contribute to the theory of composite optimization in vector spaces because the stochastic order relations are defined by a continuum of compositions of convex non-smooth functions with possibly non-convex smooth functions.
Implications for portfolio optimization will be discussed.
1766_sdc.pdf
Speaker: Darinka Dentcheva
Institution: Stevens Institute of Technology
Event Organizer: Erhan Bayraktar erhan@umich.edu
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