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1544Sherman-Morrison Vector Update D 4Suppose A is invertible, A (-1)b = [1, 3] T, A (-1)u = [0, 2] T, v T A (-1)b = 4, and v T A (-1)u = 2/3. What is (A + u v T) (-1) b?数学困难数值题未尝试面试订阅1778Lasso Threshold Calibration 3In an orthonormal lasso update, a coordinate has score z = 2.6 and penalty lambda = 1.1. What coefficient results after soft-thresholding?统计中等数值题未尝试免费1989Maximum Alpha Under a Quadratic Risk Budget 19What is the maximum value of mu 1 x + mu 2 y subject to a x 2 + b y 2 = R 2?数学困难derivation未尝试面试订阅3076Fusing Two Noisy Dealer QuotesA latent scalar state has prior N(0,9). Two conditionally independent sensors observe y 1=2 with noise variance 4 and y 2=-1 with noise variance 5. Compute the posterior mean and posterior variance after both observations.统计中等derivation未尝试面试订阅3077Two-Sensor Latent Level EstimateA latent scalar state has prior N(5,16). Two conditionally independent sensors observe y 1=9 with noise variance 9 and y 2=3 with noise variance 4. Compute the posterior mean and posterior variance after both observations.统计中等derivation未尝试面试订阅3078Dual Feed State CombinationA latent scalar state has prior N(-2,25). Two conditionally independent sensors observe y 1=-1 with noise variance 1 and y 2=2 with noise variance 4. Compute the posterior mean and posterior variance after both observations.统计中等derivation未尝试面试订阅4041Two-Asset Diagonal Kelly Vector 1Under the quadratic Kelly approximation with diagonal covariance, variances are (0.36, 0.25) and optimal weights are (0.25, 0.2). If mu 1 = 0.09, what mu 2 is implied?金融与交易中等derivation未尝试面试订阅4042Two-Asset Diagonal Kelly Vector 2Under diagonal Sigma, expected excess returns are (0.08, 0.06) and optimal weights are (0.2, 0.375). If variance of asset 2 is 0.16, what variance of asset 1 is implied?金融与交易中等derivation未尝试面试订阅4043Two-Asset Diagonal Kelly Vector 3With diagonal covariance, expected excess returns are (0.07, 0.03) and optimal weights are (0.2, 0.15). If variance of asset 1 is 0.35, what variance of asset 2 is implied?金融与交易中等derivation未尝试面试订阅4044Two-Asset Diagonal Kelly Vector 4Diagonal covariance has variances (0.25, 0.09), and the optimal Kelly vector is (0.24, -0.1). What expected excess return vector mu is implied?金融与交易中等derivation未尝试面试订阅4045Two-Asset Diagonal Kelly Vector 5With diagonal covariance, mu 1 = 0.05, variance 1 = 0.25, and variance 2 = 0.16. What mu 2 makes the total optimal gross leverage equal 0.5 if both weights are nonnegative?金融与交易中等derivation未尝试面试订阅4046Correlated Two-Asset Kelly Vector 1Under quadratic Kelly, mu = (0.08, 0.05) and Sigma = [[0.25, 0.04], [0.04, 0.16]]. What is the unconstrained optimal Kelly vector?金融与交易困难derivation未尝试面试订阅4047Correlated Two-Asset Kelly Vector 2Under quadratic Kelly, mu = (0.1, 0.04) and Sigma = [[0.36, -0.06], [-0.06, 0.25]]. What is the unconstrained optimal Kelly vector?金融与交易困难derivation未尝试面试订阅4048Correlated Two-Asset Kelly Vector 3Under quadratic Kelly with two assets, mu = (0.09, 0.03), variances are (0.36, 0.16), and covariance is c. What covariance c makes the second optimal Kelly weight exactly zero?金融与交易困难derivation未尝试面试订阅4049Correlated Two-Asset Kelly Vector 4If Sigma = [[0.25, 0.05], [0.05, 0.36]] and the optimal Kelly vector is (0.2, 0.1), what expected excess return vector mu is implied?金融与交易困难derivation未尝试面试订阅4050Correlated Two-Asset Kelly Vector 5Suppose mu = (0.068, 0.05), variances are (0.25, 0.16), and the desk wants the unconstrained Kelly optimum to be exactly (0.2, 0.2). What covariance c makes that true?金融与交易困难derivation未尝试面试订阅4051Hedge-Like Asset in Vector Kelly 1Under quadratic Kelly, mu = (0.06, 0.01) and Sigma = [[0.16, -0.03], [-0.03, 0.09]]. What is the optimal Kelly vector?金融与交易困难derivation未尝试面试订阅4054Hedge-Like Asset in Vector Kelly 4Under quadratic Kelly, mu = (0.08, 0.05) and Sigma = [[0.25, 0.04], [0.04, 0.16]]. By how much does positive covariance reduce the first Kelly weight relative to ignoring covariance?金融与交易困难derivation未尝试面试订阅4055Hedge-Like Asset in Vector Kelly 5Under quadratic Kelly, mu = (0.09, 0.04) and Sigma = [[0.25, 0.14], [0.14, 0.36]]. What is the optimal Kelly vector?金融与交易困难derivation未尝试面试订阅