2020/08/22 by Anand Deo, Deo, Anand, Karthyek Murthy +1
Decision Sciences · Mathematics · #FOS: Computer and information sciences #FOS: Economics and business #Methodology (stat.ME) #Portfolio Management (q-fin.PM) #Risk Management (q-fin.RM) #Risk and Portfolio Optimization #Statistical Methods and Inference #Statistical and numerical algorithms
paper · pdf · doi:10.48550/arxiv.2008.09818
openalex publication_date 2020/08/22 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
Motivated by the prominence of Conditional Value-at-Risk (CVaR) as a measure\nfor tail risk in settings affected by uncertainty, we develop a new formula for\napproximating CVaR based optimization objectives and their gradients from\nlimited samples. A key difficulty that limits the widespread practical use of\nthese optimization formulations is the large amount of data required by the\nstate-of-the-art sample average approximation schemes to approximate the CVaR\nobjective with high fidelity. Unlike the state-of-the-art sample average\napproximations which require impractically large amounts of data in tail\nprobability regions, the proposed approximation scheme exploits the\nself-similarity of heavy-tailed distributions to extrapolate data from suitable\nlower quantiles. The resulting approximations are shown to be statistically\nconsistent and are amenable for optimization by means of conventional gradient\ndescent. The approximation is guided by means of a systematic\nimportance-sampling scheme whose asymptotic variance reduction properties are\nrigorously examined. Numerical experiments demonstrate the superiority of the\nproposed approximations and the ease of implementation points to the\nversatility of settings to which the approximation scheme can be applied.\n