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5079Choose the Greedy Backup Action 14In one state, action 1 gives immediate reward 0.8 and then moves to states of value 6 with probability 0.2 and 1 otherwise. Action 2 gives immediate reward 0.5 and then moves to states of value 2 with probability 0.5 and 3 otherwise. If gamma=0.75, which action is greedy and what backup value does it produce?机器学习中等数值题未尝试面试订阅5491Two-Round Opportunity Value 1In round 1, a quote has fill probability 0.3 and edge 0.02 if filled. If it does not fill, you get a round-2 opportunity with fill probability 0.25 and edge 0.028. Assume a round-1 fill ends the game because your risk limit is used up. What is total expected edge?金融与交易中等数值题未尝试面试订阅5496Fill With Carry Cost 1Round 1 has fill probability 0.32 and edge 0.024, but a round-1 fill also creates carry cost 0.006 before the next decision point. If round 1 does not fill, round 2 has fill probability 0.28 and edge 0.02. What is total expected edge?金融与交易中等数值题未尝试面试订阅5501Choose First-Round Policy 1Policy A has round-1 fill probability 0.42, round-1 edge 0.012, and continuation value 0.009 if unfilled. Policy B has round-1 fill probability 0.25, round-1 edge 0.024, and continuation value 0.015 if unfilled. Which policy has higher expected value?金融与交易中等数值题未尝试面试订阅5506Two-Round Signal Tree 1Round 1 has fill probability 0.28 and edge 0.02. If round 1 does not fill, round 2 begins. At round 2 a strong signal arrives with probability 0.4; under a strong signal the quote has fill probability 0.35 and edge 0.03, while under a weak signal the fill probability is 0.2 and edge is 0.012. What is total expected edge?金融与交易困难数值题未尝试面试订阅5511Why Future Opportunity Is Part Of The Quote DecisionWhy can a quote with slightly lower immediate edge still be better once future opportunity is considered?金融与交易中等essay未尝试面试订阅5512Why Early Fill Is Not Always GoodWhy is an early fill not automatically good news in a multi-round market-making problem?金融与交易中等essay未尝试面试订阅5513Why Path Dependence MattersWhy can two strategies with the same average one-period edge have different multi-round values?金融与交易中等essay未尝试面试订阅5514Why Risk Limits Change The First QuoteWhy do tight inventory or capital limits make the first quote in a sequence more selective?金融与交易中等essay未尝试面试订阅5515Why Multi-Round Policies Need SimulationWhy is backtesting a multi-round quoting policy usually more naturally done path by path instead of only through average per-quote metrics?金融与交易中等essay未尝试面试订阅5621Tree Hedge Ratio 1At a one-step node, the underlying can move from 100 to 110 or 90. The option value in those two states is 12 and 2. What delta and cash position replicate the option over this step?数理金融中等数值题未尝试面试订阅5624Tree Hedge Ratio 4At a one-step node, the underlying can move from 95 to 109.25 or 83.6. The option value in those two states is 9.5 and 1.5. What delta and cash position replicate the option over this step?数理金融中等数值题未尝试面试订阅5626Two-Step Binomial Call 1Use a two-step binomial tree with spot 100, strike 100, up factor 1.1, down factor 0.9, rate 0.03, and step size Δt=0.5. What is the European call price at time 0?数理金融中等数值题未尝试面试订阅5628Two-Step Binomial Call 3Use a two-step binomial tree with spot 120, strike 115, up factor 1.08, down factor 0.94, rate 0.02, and step size Δt=1. What is the European call price at time 0?数理金融中等数值题未尝试面试订阅5636Why Trees Handle Early Exercise WellWhy are tree methods often more natural than Black-Scholes closed form for pricing American options?数理金融中等essay未尝试面试订阅5637Why Risk-Neutral Probability Is Not A ForecastWhy should the binomial-tree risk-neutral probability not be interpreted as your actual forecast of an up move?数理金融中等essay未尝试面试订阅5638Why More Steps HelpWhy does increasing the number of steps in a recombining tree often improve pricing accuracy?数理金融中等essay未尝试面试订阅5639Why Trees Beat Monte Carlo For Early ExerciseWhy can a simple lattice be more useful than plain Monte Carlo when exercise timing matters?数理金融中等essay未尝试面试订阅5640Why Recombining Structure MattersWhy is a recombining lattice computationally attractive compared with a tree that branches without recombining?数理金融中等essay未尝试面试订阅5677Three-Pile Nim Winning MoveTwo players play standard Nim with three piles of sizes 3, 5, and 7. On a turn a player removes any positive number of stones from a single pile, and the player who takes the last stone wins. Does the first player win, and if so, give a winning first move (which pile and how many stones to remove).脑筋急转弯简单数值题未尝试免费