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5352Compare Kelly Allocations 2Trade A wins net 0.9 with probability 0.62. Trade B wins net 3.2 with probability 0.34. Compute both full-Kelly fractions and identify which trade gets the larger capital fraction if you size them separately.金融与交易中等数值题未尝试面试订阅5356Kelly After Trading Frictions 1A trade risks 1 unit. If it wins, it earns gross 1.2 but pays a fee of 0.05. If it loses, it loses the 1 unit and still pays the same fee. The win probability estimate is 0.56. What full-Kelly fraction is optimal?金融与交易困难数值题未尝试面试订阅5357Kelly After Trading Frictions 2A trade risks 1 unit. If it wins, it earns gross 2 but pays a fee of 0.03. If it loses, it loses the 1 unit and still pays the same fee. The win probability estimate is 0.48. What full-Kelly fraction is optimal?金融与交易困难数值题未尝试面试订阅5361Why Overbetting Hurts More Than UnderbettingWhy is betting above full Kelly usually worse for long-run growth than betting the same distance below full Kelly?金融与交易中等essay未尝试面试订阅5362Why Edge Uncertainty Shrinks SizeEven if your point estimate suggests a positive full-Kelly fraction, why might a real desk still scale down the position materially?金融与交易中等essay未尝试面试订阅5363Same Expected Value Different KellyTwo trades can have similar expected value per dollar risked but very different full-Kelly fractions. Why?金融与交易中等essay未尝试面试订阅5364Why a Leverage Cap BindsWhy can a leverage cap matter even when the theoretical full-Kelly fraction is well below 100% on one trade?金融与交易中等essay未尝试面试订阅5365Why Zero Kelly Can Be CorrectWhat kinds of changes can turn a seemingly attractive trade into a zero-Kelly trade without flipping the raw headline narrative?金融与交易中等essay未尝试面试订阅5751Kelly Fraction From Edge and OddsA binary bet pays net odds of 3-to-1 (you net 3 units per unit staked on a win, lose your stake on a loss). Your win probability estimate is 0.40. What full-Kelly fraction of capital should you stake?金融与交易简单数值题未尝试免费5752Even-Money Kelly FractionYou can repeatedly take an even-money bet (win 1 unit per unit staked, or lose your stake) that you believe wins with probability 0.55. What full-Kelly fraction of capital maximizes long-run growth, and what simple expression gives it for any even-money win probability p?金融与交易简单数值题未尝试免费5753Log-Growth Rate at Full KellyFor a repeatable even-money bet that wins with probability 0.60, you bet the full-Kelly fraction. What is the resulting expected log-growth rate per round (use natural log)?金融与交易中等数值题未尝试免费5754Growth Retained at Half-KellyFor a repeatable even-money bet winning with probability 0.60, full Kelly stakes 0.20 of capital. If instead you bet half-Kelly (0.10 of capital), what fraction of the full-Kelly expected log-growth rate do you retain? Give the ratio as a decimal.金融与交易中等数值题未尝试免费5755Kelly With Asymmetric Win and Loss SizesA single bet, if it wins, gains 2 units per unit staked; if it loses, it loses only 0.5 units per unit staked. Win and loss are each 50% likely. What full-Kelly fraction of capital maximizes expected log growth?金融与交易中等数值题未尝试免费5756Growth Rate at a Chosen Overbet FractionA repeatable even-money bet wins with probability 0.60 (full-Kelly fraction is 0.20). A trader instead stakes a fixed 0.30 of capital every round. What is his expected log-growth rate per round, and is it above or below the full-Kelly rate? Give the growth rate as a decimal.金融与交易中等数值题未尝试免费5757Kelly Capped by a Max-Loss LimitA binary bet pays net odds 2-to-1 and you estimate a win probability of 0.60, giving a full-Kelly fraction of 0.40. House policy forbids risking more than 25% of capital on a single position. Since a loss costs the full stake, what fraction should you actually bet, and how is it determined?金融与交易中等数值题未尝试免费5758Sensitivity of Kelly Fraction to the EdgeFor a binary bet at net odds b=2, the full-Kelly fraction is f*=(bp-q)/b. By how much does f* change per 0.01 increase in the estimated win probability p? Give the derivative df*/dp and the change for a 0.01 move.金融与交易中等数值题未尝试免费5759Kelly Sizing When the Win Probability Is UncertainFor an even-money bet you are unsure of the true win probability: it is equally likely to be 0.52 or 0.62. A colleague plugs the average estimate 0.57 into the Kelly formula and bets 0.14 of capital. To maximize expected log growth you should instead average the realized growth over the two possible true probabilities. Set up the correct objective and state, with a brief reason, whether the growth-optimal stake is at, above, or below 0.14.金融与交易困难数值题未尝试面试订阅