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3608OU Volatility Implied by a Conditional Variance Target 3An OU process satisfies dX t = 1.4(theta - X t)dt + sigma dW t. If Var(X 0.5 | X 0) should equal 0.6, what sigma is required?随机过程中等derivation未尝试面试订阅3611Discounted GBM DynamicsA GBM satisfies dS t = 0.05 S t dt + 0.2 S t dW t. Define Y t = e -0.05 t S t. What SDE does Y t satisfy?随机过程中等derivation未尝试面试订阅3612Log of GBMA GBM satisfies dS t = 0.08 S t dt + 0.3 S t dW t. If Y t = log S t, what drift and diffusion coefficients does Y t have?随机过程中等derivation未尝试面试订阅3613Centered OU DynamicsAn OU process satisfies dX t = 1.4(3 - X t)dt + 0.7 dW t. If Y t = X t - 3, what SDE does Y t satisfy?随机过程中等derivation未尝试面试订阅3614OU Integrating-Factor TransformAn OU process satisfies dX t = 0.9(2 - X t)dt + 1.1 dW t. If Z t = e 0.9 t (X t - 2), what SDE does Z t satisfy?随机过程中等derivation未尝试面试订阅3615CIR Exponential RescalingA CIR process satisfies dX t = 1.2(4 - X t)dt + 0.5 sqrt(X t)dW t. If Y t = e 1.2 t X t, what SDE does Y t satisfy?随机过程中等derivation未尝试面试订阅3616Quadratic Variation of 2W_t Plus a Smooth DriftLet X t = 2W t + t 3 - sin t. What is [X] 2?随机过程中等derivation未尝试面试订阅3617Quadratic Variation of -3W_t Plus an Exponential TrendLet X t = -3W t + e t. What is [X] 1?随机过程中等derivation未尝试面试订阅3618Quadratic Variation of 0.5W_t Plus an Integrated DriftLet X t = 0.5W t + integral 0 t s ds. What is [X] 4?随机过程中等derivation未尝试面试订阅3619Quadratic Variation of Brownian Motion with Two Smooth CorrectionsLet X t = W t - t + cos t. What is [X] 3?随机过程中等derivation未尝试面试订阅3620Quadratic Variation of 1.2W_t Plus a Rational DriftLet X t = 1.2W t + t/(1+t). What is [X] 5?随机过程中等derivation未尝试面试订阅3621Quadratic Variation of an Itô Integral with Linear LoadingLet X t = integral 0 t (1+s) dW s. What is [X] 2?随机过程中等derivation未尝试面试订阅3622Quadratic Variation of an Itô Integral with Descending LoadingLet X t = integral 0 t (2-s) dW s. What is [X] 1?随机过程中等derivation未尝试面试订阅3623Quadratic Variation of a Piecewise-Volatility IntegralLet X t = integral 0 t sigma(s) dW s where sigma(s)=1 on [0,1], sigma(s)=2 on (1,2], and sigma(s)=0 on (2,3]. What is [X] 3?随机过程中等derivation未尝试面试订阅3624Quadratic Variation of a Square-Root LoadingLet X t = integral 0 t sqrt(1+s) dW s. What is [X] 3?随机过程中等derivation未尝试面试订阅3625Quadratic Variation of a Rescaled Time Polynomial LoadingLet X t = integral 0 t (s/3) dW s. What is [X] 3?随机过程中等derivation未尝试面试订阅3626Covariation of W_t+2B_t with 3W_t-B_tLet X t = W t + 2B t and Y t = 3W t - B t where W and B are independent Brownian motions. What is [X,Y] 1?随机过程中等derivation未尝试面试订阅3627Covariation of 2W_t-B_t with W_t+4B_tLet X t = 2W t - B t and Y t = W t + 4B t with independent W and B. What is [X,Y] 2?随机过程中等derivation未尝试面试订阅3628Covariation of 0.5W_t+B_t with 3W_t+2B_tLet X t = 0.5W t + B t and Y t = 3W t + 2B t with independent W and B. What is [X,Y] 4?随机过程中等derivation未尝试面试订阅3629Covariation of W_t-B_t with W_t+B_tLet X t = W t - B t and Y t = W t + B t with independent W and B. What is [X,Y] 3?随机过程中等derivation未尝试面试订阅