Central limit theorems for risk averse optimization problems

Resumo

We study statistical properties of the sample average approximation (SAA) of risk averse stochastic problems. We first introduce some background material, recalling important results for the continuation, such as the Delta Theorem, the Functional Central Limit Theorem, and asymptotics of risk-neutral problems. We also recall the concept of risk measures, focusing on two classes of risk measures: extended polyhedral risk measures (EPRMs) and law invariant coherent risk measures. We then provide central limit theorems for SAA estimators of the optimal values of stochastic programs expressed in terms of EPRMs or law invariant coherent risk measures, under certain assumptions on these risk measures. Numerical simulations illustrate the theoretical results.

Ficha do documento

Tipo

Dissertação

Ano

2017

Instituição

Fundação Getulio Vargas

Fonte

Repositório da FGV

Idioma

Inglês

Acesso

Não informado

Identificador

oai:repositorio.fgv.br:10438/18174

Palavras-chave

Programação estocásticaOtimização matemáticaAdministração de riscoMatemáticaAdministração de risco - Modelos matemáticos