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6049Quadratic Variation of a Stochastic IntegralDefine X t = integral from 0 to t of W s dW s. Compute the quadratic variation [X] T at T = 4, expressed as E[[X] T] (i.e. the expected accumulated quadratic variation).随机过程困难数值题未尝试面试订阅6050Closed-Form Solution of a Linear Multiplicative SDESolve the SDE dX t = a X t dt + b X t dW t with X 0 given, where a and b are constants. Write the explicit closed-form expression for X t.随机过程中等derivation未尝试免费6051Martingale Condition for W Squared Minus c tLet W t be standard Brownian motion. For what constant c is the process M t = W t 2 - c t a martingale?随机过程中等数值题未尝试免费6052Direction of Mean Reversion in a CIR ProcessA CIR process satisfies dX t = 2(0.04 - X t) dt + 0.1 sqrt(X t) dW t. The current value is X t = 0.07. Is the instantaneous drift positive or negative, and what is its numerical value?随机过程简单数值题未尝试免费6053SDE for the Exponential of Brownian MotionLet W t be standard Brownian motion and define Y t = e W t . Use Ito's lemma to find the SDE satisfied by Y t.随机过程简单derivation未尝试免费