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4891Capital Aggregation Diagnostic 1A CRO wants one firm-wide capital number for two desks whose books can offset each other. Which coherence property should you check first if you do not want the merged capital to exceed the sum of standalone capitals?数理金融中等essay未尝试面试订阅4892Capital Aggregation Diagnostic 2Treasury injects a deterministic cash buffer into every scenario of a loss distribution. Which coherence property tells you how the required capital should move after that cash injection?数理金融中等essay未尝试面试订阅4893Capital Aggregation Diagnostic 3A PM doubles every position in a book and wants to know whether capital should double too. Which coherence property is the first one to inspect?数理金融中等essay未尝试面试订阅4894Capital Aggregation Diagnostic 4Book X never loses more than book Y in any scenario. Which coherence axiom says X should not require more capital than Y?数理金融中等essay未尝试面试订阅4895Capital Aggregation Diagnostic 5Two books are each acceptable on their own under a coherent capital rule. Why should a convex mixture of the two also be acceptable?数理金融中等essay未尝试面试订阅4896Translation-Invariant Capital Recovery 6A coherent capital rule reports rho(L-h)=4.6 after a deterministic hedge h=1.2 is added in every scenario. What was rho(L), and how much extra deterministic cash would still be needed to make the hedged position acceptable?数理金融简单数值题未尝试面试订阅4897Translation-Invariant Capital Recovery 7A book has coherent capital rho(L)=7.1. Treasury wants the post-cash capital to be 2.3. How large a deterministic cash injection is needed, and how much total deterministic cash would make the original book acceptable?数理金融简单数值题未尝试面试订阅4898Translation-Invariant Capital Recovery 8A desk starts with coherent capital rho(L)=4.4. After Treasury injects exactly enough deterministic cash to leave residual capital 0.9, how much cash was injected? If Treasury had injected only 3.0 instead, what residual capital would have remained?数理金融简单数值题未尝试面试订阅4899Translation-Invariant Capital Recovery 9The amount of deterministic capital needed to make a position acceptable is 3.9. After adding a guaranteed scenario-by-scenario recovery h, the coherent capital drops to 1.6. What recovery h was added?数理金融简单数值题未尝试面试订阅4900Translation-Invariant Capital Recovery 10A loss book has coherent capital 9.6. One deterministic hedge of size 1.8 is already in place. What residual capital remains? If the desk wants residual capital 5.0 instead, how much larger must the deterministic hedge be in total?数理金融简单数值题未尝试面试订阅4903Worst-Case Hedge Design 13Desk A has scenario losses [3, 2, 7, 1] and desk B has [1, 0, 2, 5]. Under rho(L)=max scenario loss, a hedge pays h only in scenario 3. What minimum h is needed so the combined capital becomes 6?数理金融中等数值题未尝试面试订阅4905Worst-Case Hedge Design 15Desk A has scenario losses [5, 3, 1, 4] and desk B has [1, 2, 0, 3]. Under rho(L)=max scenario loss, a hedge pays h only in scenario 4. What minimum h makes the combined capital drop from 7 to 6?数理金融中等数值题未尝试面试订阅4906Infer Worst Tail Loss From a Spectral Quote 16A spectral risk measure applies weights [0.1, 0.2, 0.3, 0.4] to ordered losses [1, 3, 5, x] from best to worst. If the reported spectral risk is 6.2, what worst ordered loss x is implied?数理金融中等数值题未尝试面试订阅4907Infer Worst Tail Loss From a Spectral Quote 17A spectral risk measure applies weights [0.05, 0.15, 0.3, 0.5] to ordered losses [0, 2, 4, x]. If the reported spectral risk is 7.1, what x is implied?数理金融中等数值题未尝试面试订阅4908Infer Worst Tail Loss From a Spectral Quote 18A spectral risk measure applies weights [0.2, 0.2, 0.25, 0.35] to ordered losses [1, 2, 6, x]. If the risk value is 5.6, what x is implied?数理金融中等数值题未尝试面试订阅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