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3691Density Tilt Making an Energy Factor Slow Down Under QUnder P, a factor satisfies dX t = 1.1 dt + 0.5 dW t. A new measure Q is defined by W t Q = W t + theta t. What theta makes the drift of X under Q equal 0.2?随机过程中等derivation未尝试面试订阅3692Density Tilt Turning a Positive Drift into a Mild Negative OneUnder P, a factor satisfies dX t = 0.4 dt + 0.8 dW t. A new measure Q is defined by W t Q = W t + theta t. What theta makes the drift of X under Q equal -0.08?随机过程中等derivation未尝试面试订阅3693Density Tilt Removing Carry from a Basis ProcessUnder P, a factor satisfies dX t = 0.9 dt + 0.3 dW t. A new measure Q is defined by W t Q = W t + theta t. What theta makes the drift of X under Q equal 0?随机过程中等derivation未尝试面试订阅3694Density Tilt Lifting a Negative Drift Above ZeroUnder P, a factor satisfies dX t = -0.2 dt + 0.4 dW t. A new measure Q is defined by W t Q = W t + theta t. What theta makes the drift of X under Q equal 0.1?随机过程中等derivation未尝试面试订阅3696Second Factor Drift After Neutralizing the First CarryUnder P, two processes share the same Brownian driver: dX t = 1.2dt + 0.6dW t and dY t = 0.5dt + 0.25dW t. If Q is chosen so that X has drift 0.3 under Q, what drift does Y have under Q?随机过程中等derivation未尝试面试订阅3697Co-Moving Spread Drift After Re-Centering the BenchmarkUnder P, two processes share the same Brownian driver: dX t = 0.7dt + 0.4dW t and dY t = -0.2dt + 0.9dW t. If Q is chosen so that X has drift -0.1 under Q, what drift does Y have under Q?随机过程中等derivation未尝试面试订阅3698Macro Factor Drift After Removing a Reference PremiumUnder P, two processes share the same Brownian driver: dX t = 0.5dt + 0.25dW t and dY t = 0.15dt + 0.35dW t. If Q is chosen so that X has drift 0 under Q, what drift does Y have under Q?随机过程中等derivation未尝试面试订阅3700Auxiliary Process Drift After Calibrating a Target ProcessUnder P, two processes share the same Brownian driver: dX t = 0.3dt + 0.2dW t and dY t = 0.45dt + 0.1dW t. If Q is chosen so that X has drift -0.05 under Q, what drift does Y have under Q?随机过程中等derivation未尝试面试订阅3701Linear Desk PnL Drift Target from a Shared DriverUnder P, dX t = 0.8dt + 0.4dW t and dY t = 0.3dt + 0.2dW t share the same Brownian motion. Let L t = 2X t + 1Y t. If Q is chosen so that L has drift 0.6 under Q, what theta is required and what is the resulting Q-drift of X?随机过程中等derivation未尝试面试订阅3702Spread Drift Target via One Girsanov TiltUnder P, dX t = 0.7dt + 0.5dW t and dY t = 0.2dt + 0.4dW t share the same Brownian motion. Let L t = 1X t + -1Y t. If Q is chosen so that L has drift -0.1 under Q, what theta is required and what is the resulting Q-drift of X?随机过程中等derivation未尝试面试订阅3706Other Factor Drift After Making a Stock Discounted Price DriftlessA traded underlier satisfies dS t/S t = 0.09dt + 0.25dW t under P, while another factor satisfies dY t = 0.2dt + 0.4dW t with the same Brownian driver. If Q is chosen so the discounted stock has drift 0 at rate r = 0.03, what is the drift of Y under Q?随机过程中等derivation未尝试面试订阅3707Convenience-Yield Drift Under the Pricing MeasureA traded underlier satisfies dS t/S t = 0.12dt + 0.3dW t under P, while another factor satisfies dY t = -0.1dt + 0.15dW t with the same Brownian driver. If Q is chosen so the discounted stock has drift 0 at rate r = 0.04, what is the drift of Y under Q?随机过程中等derivation未尝试面试订阅3711Why Girsanov Changes Drift but Not Instantaneous VolatilityUnder a standard Girsanov tilt, why do drift coefficients change while instantaneous diffusion loadings stay the same?随机过程中等essay未尝试面试订阅3712Same Paths, Different Weights Under P and QWhat does it mean to say that P and Q describe the same path space but assign different likelihood weights to paths?随机过程中等essay未尝试面试订阅3713Why Integrability Conditions Matter in GirsanovWhy do conditions such as Novikov's criterion matter when applying Girsanov in practice?随机过程中等essay未尝试面试订阅3714Why a Single Tilt Moves All Co-Driven Factors TogetherIf two factors share the same Brownian driver, why does calibrating the Girsanov tilt from one factor automatically change the other's drift as well?随机过程中等essay未尝试面试订阅3715Why Girsanov Is Useful for Pricing Even When Physical Drift Is InterestingWhy is Girsanov still useful in pricing problems even when a researcher cares about the physical drift of the process?随机过程中等essay未尝试面试订阅