TY - JOUR
T1 - A framework for optimization under ambiguity
AU - Wozabal, David
N1 - Funding Information:
This research was partly funded by the Vienna Science and Technology Fund (Grant: MA06) and the Austrian National Bank (Grant: 12306).
PY - 2012/3
Y1 - 2012/3
N2 - In this paper, single stage stochastic programs with ambiguous distributions for the involved random variables are considered. Though the true distribution is unknown, existence of a reference measure P̂ enables the construction of non-parametric ambiguity sets as Kantorovich balls around P̂. The original stochastic optimization problems are robustified by a worst case approach with respect to these ambiguity sets. The resulting problems are infinite optimization problems and can therefore not be solved computationally by straightforward methods. To nevertheless solve the robustified problems numerically, equivalent formulations as finite dimensional non-convex, semi definite saddle point problems are proposed. Finally an application from portfolio selection is studied for which methods to solve the robust counterpart problems explicitly are proposed and numerical results for sample problems are computed.
AB - In this paper, single stage stochastic programs with ambiguous distributions for the involved random variables are considered. Though the true distribution is unknown, existence of a reference measure P̂ enables the construction of non-parametric ambiguity sets as Kantorovich balls around P̂. The original stochastic optimization problems are robustified by a worst case approach with respect to these ambiguity sets. The resulting problems are infinite optimization problems and can therefore not be solved computationally by straightforward methods. To nevertheless solve the robustified problems numerically, equivalent formulations as finite dimensional non-convex, semi definite saddle point problems are proposed. Finally an application from portfolio selection is studied for which methods to solve the robust counterpart problems explicitly are proposed and numerical results for sample problems are computed.
KW - Difference of convex algorithm
KW - Expected shortfall
KW - Non-convex optimization
KW - Portfolio management
KW - Robust optimization
KW - Semi definite programming
UR - http://www.scopus.com/inward/record.url?scp=84855211430&partnerID=8YFLogxK
U2 - 10.1007/s10479-010-0812-0
DO - 10.1007/s10479-010-0812-0
M3 - Article
AN - SCOPUS:84855211430
SN - 0254-5330
VL - 193
SP - 21
EP - 47
JO - Annals of Operations Research
JF - Annals of Operations Research
IS - 1
ER -