Exploiting structure of autoregressive processes in risk-averse multistage stochastic linear programs
Claudia Sagastizabal | Guigues, Vincent
stochastic processes | generalized auto-regressive models | risk-averse optimization
We consider a multivariate interstage dependent stochastic process with components following a generalized autoregressive model with time varying order. At a given time step, we give some recursive formul\ae\/ linking future values of the process with past values and noises. We then consider multistage stochastic linear programs with uncertain polyhedral sets depending affinely on such processes. At each stage, when uncertainty is dealt with using probabilistic and CVaR constraints, the recursive relations can be used to obtain explicit expressions for the feasible set, making the corresponding risk-averse stochastic linear program tractable. Using these risk-averse programs (one for each stage) in a rolling-horizon mode, a risk-averse nonanticipative policy can be built.