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4911Acceptance-Set Geometry 21Why is a convex acceptance set operationally useful when two desks ask whether they can partially blend books without blowing up capital?数理金融困难essay未尝试面试订阅4912Firmwide Aggregation Intuition 22Why is subadditivity the coherence axiom desks care about most when the firm aggregates capital across books?数理金融困难essay未尝试面试订阅4913Liquidity Blind Spot 23Why can a perfectly coherent risk measure still miss a major liquidity problem on a stressed desk?数理金融困难essay未尝试面试订阅4914VaR Aggregation Critique 24Why can a VaR number look reasonable for one desk in isolation yet still be awkward as a firmwide capital aggregator?数理金融困难essay未尝试面试订阅4915Spectral Weight Design 25Why should a spectral risk measure place weakly larger weights on worse outcomes than on mild ones?数理金融困难essay未尝试面试订阅4916Infer Normal Parameters From VaR And ES 1A desk assumes losses are normal with mean mu and standard deviation sigma. At alpha=0.95 it uses VaR = mu + z*sigma and ES = mu + k*sigma with z=1.645 and k=2.063. If the reported VaR is 7.58 and ES is 9.252, what are mu and sigma?数理金融中等数值题未尝试面试订阅4917Infer Normal Parameters From VaR And ES 2A normal-loss desk uses alpha=0.99 with VaR = mu + z*sigma and ES = mu + k*sigma, where z=2.326 and k=2.665. If VaR is 7.478 and ES is 8.495, what are mu and sigma?数理金融中等数值题未尝试面试订阅4918Infer Normal Parameters From VaR And ES 3A risk report uses alpha=0.975 with z=1.96 and k=2.338 in the formulas VaR = mu + z*sigma and ES = mu + k*sigma. If VaR is 11.8 and ES is 13.69, what are mu and sigma?数理金融中等数值题未尝试面试订阅4919Infer Normal Parameters From VaR And ES 4A normal-loss desk uses alpha=0.95 with z=1.645 and k=2.063. If the reported VaR is 4.1125 and ES is 5.1575, what are mu and sigma?数理金融中等数值题未尝试面试订阅4920Infer Normal Parameters From VaR And ES 5A desk uses alpha=0.99 with z=2.326 and k=2.665 in the formulas VaR = mu + z*sigma and ES = mu + k*sigma. If VaR is 15.156 and ES is 17.19, what are mu and sigma?数理金融中等数值题未尝试面试订阅4921Infer Missing Tail Observation 6Sorted empirical losses are [1, 2, 3, 4, 7, 9, 12, x]. Using alpha=0.75, define empirical VaR as the ceil(alpha*n)-th order statistic and empirical ES as the average of losses at and beyond that cutoff. If empirical ES is 11.5, what is x?数理金融中等数值题未尝试面试订阅4922Infer Missing Tail Observation 7Sorted empirical losses are [0, 1, 1, 3, 5, 6, 8, x]. Using alpha=0.875 with the same empirical VaR and ES conventions, if empirical ES is 9.5, what is x?数理金融中等数值题未尝试面试订阅4923Infer Missing Tail Observation 8Sorted empirical losses are [2, 2, 4, 5, 7, 10, 13, x]. Using alpha=0.75 and the same conventions, if empirical ES is 15, what is x?数理金融中等数值题未尝试面试订阅4924Infer Missing Tail Observation 9Sorted empirical losses are [1, 1, 2, 4, 4, 7, 9, x]. Using alpha=0.875 and the same conventions, if empirical ES is 11.5, what is x?数理金融中等数值题未尝试面试订阅4926Infer One-Day VaR From Multi-Day Scaling 11Under square-root-of-time Gaussian scaling, a 10-day VaR is 7.589466. What 1-day VaR does that imply?数理金融中等数值题未尝试面试订阅4928Infer Pareto Tail Index From ES To VaR Ratio 13For a Pareto tail, suppose ES/VaR = alpha/(alpha-1). If VaR is 8 and ES is 12, what tail index alpha is implied?数理金融中等数值题未尝试面试订阅4929Infer Pareto Tail Index From ES To VaR Ratio 14For a Pareto tail with ES/VaR = alpha/(alpha-1), if VaR is 5.5 and ES is 9.166667, what alpha is implied?数理金融中等数值题未尝试面试订阅4931Infer Portfolio Covariance Loading From Component VaR 16For a linear Gaussian portfolio, component VaR satisfies component i = w i * z alpha * (Sigma w) i / sigma p. If z alpha=1.645, sigma p=0.2, w i=0.6, and the reported component VaR is 0.11844, what covariance loading (Sigma w) i is implied?数理金融困难数值题未尝试面试订阅4932Infer Portfolio Covariance Loading From Component VaR 17For a linear Gaussian portfolio, z alpha=2.326, sigma p=0.3, w i=0.35, and the reported component VaR is 0.111260333. What covariance loading (Sigma w) i is implied?数理金融困难数值题未尝试面试订阅4933Infer Portfolio Covariance Loading From Component VaR 18For a linear Gaussian portfolio, z alpha=1.96, sigma p=0.25, w i=0.5, and the component VaR is 0.1176. What covariance loading (Sigma w) i is implied?数理金融困难数值题未尝试面试订阅