Risk-averse Stochastic Vector Optimization
Yrd. Doç. Dr. Çağın Ararat, IE, Bilkent
March 30, Friday 13:30
Two-stage risk-averse stochastic optimization is concerned with the minimization of a risk measure of a random cost function over the feasible choices of a deterministic (first stage) and a random (second stage) decision variable. We study the multi-objective version of this problem in which case the cost function is vector-valued and its risk is quantified via a set-valued risk measure. The proposed formulation is a convex vector optimization problem with set-valued constraints. To approximate the set of all Pareto efficient solutions of this problem, we propose customized versions of Benson’s algorithm. In particular, by randomizing the first-stage decision variable, we develop convex duality-based decomposition methods to find dual solutions to the scalar subproblems appearing in Benson’s algorithm and a final procedure to recover primal solutions from the dual ones. The computational methods are tested on a multi-asset portfolio optimization problem with transaction costs.
Short Bio of the speaker
Çağın Ararat is an Assistant Professor in the Department of Industrial Engineering at Bilkent University. He received his BS degree in 2010 from the same department, followed by a PhD degree in 2015 from the Department of Operations Research and Financial Engineering at Princeton University. His research interests include vector- and set-valued functions in financial mathematics, multivariate risk, systemic risk and stochastic optimization. He is a member of SIAM, INFORMS and AMS.