Structure of risk-averse multistage stochastic programs

Abstrakt

We deal with risk-averse multistage stochastic programs with coherent risk measures such as multiperiod extensions of conditional value at risk or polyhedral risk measures. Their basic properties are discussed and applied to scenario-based input data.

Using the contamination technique we quantify the influence of changes in the structure of the scenario-based approximation to the optimal value of the problem. Stochastic dual dynamic programming algorithm is used to provide illustrative numerical comparisons for different choices of risk measures and changes of input data for a simple multistage risk-averse stock allocation problem with scenario trees based on log-normal distribution of the asset returns.

Klíčová slova

• Multistage stochastic programming
• Multiperiod risk measures
• Stochastic dual dynamic programming
• Contamination