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1870RW Versus MR Diagnosis 5A desk notices that expected residual carry from holding a spread for longer horizons quickly saturates instead of growing linearly forever. Is that more consistent with random walk or mean reversion?统计困难derivation未尝试面试订阅1919Look-Ahead Audit Scenario 4A training set includes observations whose labels use returns that overlap with the future test window. What should be added to the split procedure?统计中等数值题未尝试面试订阅1962Balanced Exponential Penalties 17A desk minimizes J(x)=6 e x + 3 e -2x . What x is optimal?数学中等derivation未尝试免费1973How the Cheap Book Gets More Size 3In the problem min a x 2 + b y 2 subject to x+y=c, which book gets the larger allocation when a<b, and why?数学中等derivation未尝试免费1977Derive the Three-Book Total-Size Allocation 7Derive the minimizer of a x 2 + b y 2 + c z 2 subject to x+y+z=N for positive a,b,c.数学中等derivation未尝试免费1980Minimum Risk Needed for a Target Alpha 10A desk wants to minimize a x 2 + b y 2 subject to mu 1 x + mu 2 y = A. What is the minimum achievable value?数学困难derivation未尝试面试订阅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1991Zero Alpha Target Implies Zero Minimum Risk 21If the target alpha level A in mu 1 x + mu 2 y = A is zero, what is the minimum of a x 2 + b y 2?数学中等derivation未尝试免费2028Log Carry Score Is Concave 8Let psi(x)=ln(1+x) on x>-1. Compare E[psi(X)] and psi(E[X]).数学中等derivation未尝试面试订阅2030Recovering Scenario Weights From a Concave Impact Average 10Let V take values 0 and 3, with probabilities p and 1-p. If E[sqrt(1+V)] = 5/4, determine p and then compute sqrt(1+E[V]).数学中等derivation未尝试面试订阅2033Certainty-Equivalent Return From Expected Log Growth 13A strategy produces one-period returns of 0% or 60%, each with probability 1/2 on one dollar of wealth. Compute E[ln(1+R)] and the certainty-equivalent constant return r ce satisfying ln(1+r ce)=E[ln(1+R)].数学中等derivation未尝试面试订阅2037Why Jensen Matters for Nonlinear Risk Transforms 17Why is it dangerous to plug an average state into a nonlinear convex risk transform and treat that as the average transformed risk?数学中等essay未尝试面试订阅2045Comparing Two Equal-Mean Schedules Under an Alternative Surcharge 25A utilization surcharge is c(q)=1/(2-q) on q<2. Schedule A is deterministic with Q=1. Schedule B uses Q=1/2 or 3/2 with probability 1/2 each. Compute E[c(Q)] for Schedule B and c(E[Q]) for the shared mean.数学困难数值题未尝试面试订阅2296Jump Compensator Recovery 1A desk uses the simplified risk-neutral drift relation mu Q = r - lambda*kappa for a jump-diffusion. If r = 3.00%, lambda = 1.2, and mu Q = 0.60%, what jump compensator kappa is implied?数理金融简单数值题未尝试免费2297Jump Compensator Recovery 2In a simplified jump-diffusion, mu Q = r - lambda*kappa. If r = 2.50%, kappa = 1.60%, and mu Q = 0.50%, what jump intensity lambda is implied?数理金融简单数值题未尝试免费2298Jump Compensator Recovery 3A risk-neutral jump-diffusion uses mu Q = r - lambda*kappa. If r = 4.00%, lambda = 0.8, and kappa = 1.00%, what is mu Q?数理金融简单数值题未尝试免费2299Jump Compensator Recovery 4A desk writes the compensated jump-diffusion drift as mu Q = r - lambda*kappa. If mu Q = 0.60%, lambda = 1.5, and kappa = -0.40%, what risk-free rate r is consistent with that setup?数理金融简单数值题未尝试免费2300Jump Compensator Recovery 5A desk uses the simplified risk-neutral drift relation mu Q = r - lambda*kappa for a jump-diffusion. If r = 1.50%, lambda = 2, and mu Q = -0.30%, what jump compensator kappa is implied?数理金融简单数值题未尝试免费2301Poisson Jump Calibration 1In a jump-diffusion with Poisson intensity lambda, the probability of zero jumps over horizon T is exp(-lambda*T). If the no-jump probability over T = 1 years is 0.36, what lambda is implied?数理金融简单数值题未尝试免费2302Poisson Jump Calibration 2The probability of at least one jump over horizon T in a Poisson jump model is 1-exp(-lambda*T). If that probability is 0.451188 over T = 1.5 years, what lambda is implied?数理金融简单数值题未尝试免费