2021/01/07 by Alois Pichler, Alexander Shapiro, Pichler, Alois +1 · 2 citations
Agricultural and Biological Sciences · Decision Sciences · Economics, Econometrics and Finance · #60B05 #62P05 #90C08 #90C15 #90C31 #Agricultural risk and resilience #FOS: Mathematics #Insurance and Financial Risk Management #Optimization and Control (math.OC) #Risk and Portfolio Optimization
paper · pdf · doi:10.48550/arxiv.2101.02498
openalex publication_date 2021/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Distributionally robust optimization involves various probability measures in\nits problem formulation. They can be bundled to constitute a risk functional.\nFor this equivalence, risk functionals constitute a fundamental building block\nin distributionally robust stochastic programming. Multistage programming\nrequires conditional versions of risk functionals to re-assess future risk\nafter partial realizations and after preceding decisions.\n This paper discusses a construction of the conditional counterpart of a risk\nfunctional by passing its genuine characteristics to its conditional\ncounterparts. The conditional risk functionals turn out to be different from\nthe nested analogues of the original (law invariant) risk measure. It is\ndemonstrated that the initial measure and its nested decomposition can be used\nin a distributionally robust multistage setting.\n