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4485First DiagnosticIn a simple discrete model, what is the first thing you should check before talking about arbitrage-free pricing measures?数理金融中等essay未尝试面试订阅4486Before Solving ProbabilitiesBefore solving for a risk-neutral probability, what inequality should you inspect first in a one-period model?数理金融中等essay未尝试面试订阅4506Why Counting Securities Is Not Enough for CompletenessA candidate says a 4-state market with 4 traded securities must be complete. Why is that claim too quick?数理金融中等essay未尝试面试订阅4507Why a Redundant Asset Does Not Collapse a Pricing IntervalIn an incomplete market, why does listing one more asset fail to eliminate price intervals if that asset's payoff lies in the old span?数理金融中等essay未尝试面试订阅4508Why an Incomplete Market Can Still Uniquely Price One ClaimWhy can a market be globally incomplete yet still assign a unique arbitrage-free price to one particular claim?数理金融中等essay未尝试面试订阅4509Why Strict Positivity Matters When Talking About Equivalent MeasuresWhy is strict positivity of state prices or implied probabilities part of the theorem's language rather than a cosmetic side condition?数理金融中等essay未尝试面试订阅4510Why Uniqueness of the Pricing Measure and Completeness Tell the Same Geometry StoryAt interview level, why should you think of 'unique martingale measure' and 'complete market' as two views of the same linear-algebra fact?数理金融中等essay未尝试面试订阅4511Why Price Intervals Come from Missing DirectionsWhy do arbitrage-free price intervals typically appear when the traded span misses some state-space directions?数理金融中等essay未尝试面试订阅4512What to Challenge First When Someone Says 'Three Securities, Three States, So Complete'A PM says 'there are three securities and three states, so the market is complete.' What is the first structural check you should push back with?数理金融中等essay未尝试面试订阅4513Why Attainability Comes Before Probability LanguageIf a nontraded claim seems to have several candidate prices, what should you verify before arguing about which probability measure is 'correct'?数理金融中等essay未尝试面试订阅4514Why the Same Market Can Have One Price for Replicable Claims and Many for OthersHow can one and the same market produce exact single prices for some claims and only intervals for others without contradiction?数理金融中等essay未尝试面试订阅4515Why an Extra Asset Must Add a New Direction, Not Just a New StoryWhen someone claims a newly listed security 'should help complete the market,' what makes that statement true or false?数理金融中等essay未尝试面试订阅4585PDE First Step 20Before launching into the PDE derivation, what tradable hedge object should you define first?数理金融中等essay未尝试面试订阅4586PDE First Step 21Before writing Ito's lemma in full, what should you specify first about the option value function?数理金融中等essay未尝试面试订阅4587PDE First Step 22Before modifying the PDE for carry or dividends, what parameter should you identify first?数理金融中等essay未尝试面试订阅4588PDE First Step 23Before trying to solve the Black-Scholes PDE, what payoff-side condition should you write first?数理金融中等essay未尝试面试订阅4589PDE First Step 24Before interpreting delta as a trading quantity, what mathematical identity should you identify first?数理金融中等essay未尝试面试订阅4605Martingale First Step 15Before carrying out any lognormal integral in the martingale derivation, what object should you isolate first?数理金融中等essay未尝试面试订阅4611Martingale First Step 16Before invoking any theorem-level pricing statement in the martingale route, what should you identify first?数理金融中等essay未尝试面试订阅4612Martingale First Step 17What should you write down first before evaluating any tail expectation for a call payoff?数理金融中等essay未尝试面试订阅