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2258Copula Desk Intuition 3Why does matching single-name spreads still leave a lot of freedom in basket-loss modeling?数理金融困难essay未尝试面试订阅2260Copula Desk Intuition 5Why is tail dependence really about bad states lining up, not just about average correlation looking high?数理金融困难essay未尝试面试订阅2261Copula Desk Intuition 6Why can a Gaussian copula fit one slice of quoted tranches and still be economically unconvincing?数理金融困难essay未尝试面试订阅2262Copula Desk Intuition 7Why do structured-credit desks still run scenario tables after calibrating a copula?数理金融困难essay未尝试面试订阅2263Copula Desk Intuition 8Why does sector concentration often break the spirit of a single-factor dependence model before the math breaks?数理金融困难essay未尝试面试订阅2264Copula Desk Intuition 9Why do attachment and detachment points turn a small change in dependence into a large change in tranche value?数理金融困难essay未尝试面试订阅2265Copula Desk Intuition 10Why can recovery assumptions and dependence assumptions interact instead of being separable knobs?数理金融困难essay未尝试面试订阅2266Copula Desk Intuition 11Why should a modeler distrust a dependence setup that implies a very benign calm regime and an absurdly catastrophic stress regime?数理金融中等essay未尝试面试订阅2267Copula Desk Intuition 12Why is nth-to-default risk more about ordering of losses than about one representative pairwise correlation?数理金融中等essay未尝试面试订阅2268Copula Desk Intuition 13Why is historical estimation of tail dependence usually much less reliable than historical estimation of calm-state default frequency?数理金融中等essay未尝试面试订阅2269Copula Desk Intuition 14Why is 'correlation smile' really a market symptom of model incompleteness rather than a literal smile of one primitive quantity?数理金融中等essay未尝试面试订阅2270Copula Desk Intuition 15Why do traders care whether a copula story is economically interpretable even if the day-one marks look fine?数理金融中等essay未尝试面试订阅2459Using Revised Index Membership in Historical FilteringA backtest filters the universe using current index membership and then evaluates historical predictions on that restricted universe. Why is this also a train/test discipline problem?机器学习困难essay未尝试面试订阅2529Why Regularization Helps Even When Logistic Is Convex 11If logistic loss is already convex, why can regularization still be crucial in practice?机器学习中等essay未尝试面试订阅2534One Gradient Step on a Tiny Logistic ProblemA one-feature logistic model without intercept uses beta = 0 initially, learning rate 0.2, data x = [-1, 0, 1], and labels y = [0, 0, 1]. What is beta after one gradient step on the negative log-likelihood?机器学习困难数值题未尝试面试订阅2537Why Logistic Probabilities Are Useful Downstream 18Why is it valuable that logistic regression produces a calibrated probability estimate rather than only a hard class label?机器学习中等essay未尝试面试订阅2610Scale-Update Invariance Between Eta and Gamma 6Why does multiplying every leaf update gamma m by c and dividing the learning rate eta by c leave the final additive score unchanged?机器学习困难derivation未尝试面试订阅4466Risk-Neutral Probability And No-Arbitrage 1In a one-period binomial model, S0=100, Su=120, Sd=90, and the simple risk-free rate is 0. Compute the risk-neutral probability of the up state, and state whether the no-arbitrage condition holds.数理金融简单数值题未尝试面试订阅4467Risk-Neutral Probability And No-Arbitrage 2In a one-period binomial model, S0=50, Su=65, Sd=45, and the simple risk-free rate is 0.05. Compute the risk-neutral probability of the up state, and state whether the no-arbitrage condition holds.数理金融简单数值题未尝试面试订阅4471State-Price Density Solve 1A stock and bond trade in a one-period two-state model with S0=100, Su=120, Sd=80, and gross risk-free return 1. Solve for the state-price densities λu and λd.数理金融中等数值题未尝试面试订阅