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Combining Retrospective Approximation with Importance Sampling for Optimising Conditional Value at Risk

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  • Anand Deo
  • Karthyek Murthy
  • Tirtho Sarker

Abstract

This paper investigates the use of retrospective approximation solution paradigm in solving risk-averse optimization problems effectively via importance sampling (IS). While IS serves as a prominent means for tackling the large sample requirements in estimating tail risk measures such as Conditional Value at Risk (CVaR), its use in optimization problems driven by CVaR is complicated by the need to tailor the IS change of measure differently to different optimization iterates and the circularity which arises as a consequence. The proposed algorithm overcomes these challenges by employing a univariate IS transformation offering uniform variance reduction in a retrospective approximation procedure well-suited for tuning the IS parameter choice. The resulting simulation based approximation scheme enjoys both the computational efficiency bestowed by retrospective approximation and logarithmically efficient variance reduction offered by importance sampling

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  • Anand Deo & Karthyek Murthy & Tirtho Sarker, 2022. "Combining Retrospective Approximation with Importance Sampling for Optimising Conditional Value at Risk," Papers 2206.12835, arXiv.org.
    • Handle: RePEc:arx:papers:2206.12835
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    References listed on IDEAS

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    1. Güzin Bayraksan & David P. Morton, 2011. "A Sequential Sampling Procedure for Stochastic Programming," Operations Research, INFORMS, vol. 59(4), pages 898-913, August.
    2. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496.
    3. Rubinstein, Reuven Y., 1997. "Optimization of computer simulation models with rare events," European Journal of Operational Research, Elsevier, vol. 99(1), pages 89-112, May.
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