第 12 / 12 页
非代码面试题
显示 15 / 235 道匹配题目
答题状态：未尝试未正确已正确
ID题目领域难度题型进度权限
3641Coefficient Making W_t^2-a t a MartingaleChoose a so that X t = W t 2 - a t is a martingale.随机过程中等derivation未尝试面试订阅3642Coefficient Making exp(aW_t-2t) a MartingaleChoose a so that X t = exp(aW t - 2t) is a martingale.随机过程中等derivation未尝试面试订阅3643Coefficient Making e^{a t} cos W_t a MartingaleChoose a so that X t = e a t cos W t is a martingale.随机过程中等derivation未尝试面试订阅3653Choose c for a Cubic Brownian Local MartingaleFor standard Brownian motion, choose c so that X t=W t 3-c\int 0 t W s\,ds is a local martingale.随机过程中等derivation未尝试面试订阅3655Choose c in the Quartic Brownian PolynomialFor standard Brownian motion, choose c so that X t=W t 4-6tW t 2+ct 2 is a martingale.随机过程中等derivation未尝试面试订阅5856Compound-Limit ExponentialEvaluate the limit of the sequence a n = (1 + 3/n) n as n -> inf. Give the exact value and a decimal to three places.数学中等数值题未尝试免费5896Why Half-Kelly Keeps Three-Quarters of the GrowthFor a small-edge repeated bet the expected log-growth is well approximated by the quadratic G(f)\approx f-\tfrac12 2 f 2, where and 2 are the per-round mean and variance of the bet's return. Using this approximation, find the optimal fraction f * and show what fraction of the maximal growth G(f *) is retained by betting half-Kelly, f=f */2.概率中等derivation未尝试面试订阅5897Overbetting to Twice KellyUnder the small-edge approximation G(f)\approx f-\tfrac12 2 f 2 for the expected log-growth of a repeated bet, the growth-optimal fraction is f *= / 2. At what (nonzero) betting fraction does the expected log-growth fall back to zero, and what does this say about the symmetry of growth around f *?概率中等数值题未尝试面试订阅5898Continuous Kelly for Normal ReturnsEach round you allocate a fraction f of wealth to a position whose one-period return R is approximately normal with small mean >0 and variance 2 (with 2\ll 2), so post-round wealth is multiplied by 1+fR. Using a second-order expansion of the log, derive the growth-optimal fraction f *.概率中等derivation未尝试面试订阅6044Differential of W_t SquaredLet W t be standard Brownian motion. Apply Ito's lemma to f(W t) = W t 2 and write the resulting SDE d(W t 2) in terms of dt and dW t.随机过程简单derivation未尝试免费6046Differential of t Times W_tLet W t be standard Brownian motion. Using the Ito product rule, find d(t W t) and express the resulting SDE in terms of dt and dW t.随机过程中等derivation未尝试免费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