Computational Management Science

, Volume 12, Issue 2, pp 221–242

# On variance reduction of mean-CVaR Monte Carlo estimators

Original Paper

## Abstract

We formulate an objective as a convex combination of expectation and risk, measured by the $$\mathrm{CVaR }$$ risk measure. The poor performance of standard Monte Carlo estimators applied on functions of this form is discussed and a variance reduction scheme based on importance sampling is proposed. We provide analytical solution for random variables based on normal distribution and outline the way for the other distributions, either by analytical computation or by sampling. Our results are applied in the framework of stochastic dual dynamic programming algorithm. Computational results which validate the previous analysis are given.

### Keywords

Importance sampling Risk-averse optimization Monte Carlo sampling Stochastic dual dynamic programming

### Mathematics Subject Classification

65C05 90C15 91G60

## Notes

### Acknowledgments

The research was partly supported by the project of the Czech Science Foundation P/402/12/G097 ‘DYME/Dynamic Models in Economics’.

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