第 1 / 6 页
非代码面试题
显示 20 / 109 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
1946Log Utility Versus Impact Budget 1A signal is strong enough that the PM scores larger size through a log benefit but pays quadratic impact. The desk chooses a scalar exposure x > -1 to maximize F(x) = 3 ln(1+x) - 2 x 2. What exposure x maximizes F?数学简单数值题未尝试免费1947Log Utility Versus Impact Budget 2A desk chooses a participation tilt with diminishing marginal benefit and quadratic implementation drag. The desk chooses a scalar exposure x > -1 to maximize F(x) = 4 ln(1+x) - 1 x 2. What exposure x maximizes F?数学简单数值题未尝试免费1948Log Utility Versus Impact Budget 3A portfolio manager sizes one smooth alpha sleeve with a log reward and a quadratic risk surcharge. The desk chooses a scalar exposure x > -1 to maximize F(x) = 12 ln(1+x) - 1 x 2. What exposure x maximizes F?数学中等数值题未尝试免费1949Derive the Optimizer for Log Utility Minus Quadratic Cost 4For parameters a>0 and b>0, derive the unique maximizer of F(x)=a ln(1+x)-b x 2 on x>-1.数学中等derivation未尝试免费1950Quarter-Size Utility Balance 5A PM uses a very steep quadratic penalty, so the optimal tilt should stay small even with positive edge. The desk chooses a scalar exposure x > -1 to maximize F(x) = 5 ln(1+x) - 8 x 2. What exposure x maximizes F?数学困难derivation未尝试免费1951Bid-Ask Skew Balance 6On one quote axis, the maker gets more value from aggressive bids than from aggressive offers. A market maker chooses a skew x in (-1,1) to maximize G(x) = 5 ln(1+x) + 3 ln(1-x). What skew is optimal?数学简单数值题未尝试免费1952Derive the Optimizer for an Asymmetric Log Skew Objective 7For a>0 and b>0, derive the unique maximizer of G(x)=a ln(1+x)+b ln(1-x) on x in (-1,1).数学中等derivation未尝试免费1953Mild Positive Skew From Asymmetric Flow 8Order-flow asymmetry is present but not extreme, so the optimal skew should stay close to flat. A market maker chooses a skew x in (-1,1) to maximize G(x) = 7 ln(1+x) + 5 ln(1-x). What skew is optimal?数学中等derivation未尝试免费1954Symmetric Flow Implies Flat Skew 9If a market maker maximizes G(x)=a ln(1+x)+a ln(1-x) on x in (-1,1), what skew is optimal?数学中等derivation未尝试免费1955Large Buy-Side Imbalance Skew 10A quoting engine values upside fill opportunities much more than downside ones, so the optimal skew should be meaningfully positive. A market maker chooses a skew x in (-1,1) to maximize G(x) = 9 ln(1+x) + 3 ln(1-x). What skew is optimal?数学困难derivation未尝试免费1956Carry Drag Versus Quadratic Inventory 11A carry term explodes as the state approaches -1, so the desk cannot simply push x downward. Minimize H(x) = 4 x 2 + 9/(1+x) over x > -1.数学简单数值题未尝试免费1957Funding Buffer Versus Risk Penalty 12A funding buffer term falls with x while the quadratic penalty rises, creating an interior optimum. Minimize H(x) = 3 x 2 + 24/(1+x) over x > -1.数学简单数值题未尝试免费1958Verify the Designed Minimizer in a Quadratic-Reciprocal Objective 13Let r>0 and a>0. Show that x=r uniquely minimizes H(x)=a x 2 + 2 a r(1+r) 2 /(1+x) over x>-1.数学中等derivation未尝试免费1959Large Cushion Interior Minimum 14The reciprocal term is strong enough that the optimum sits well away from the boundary. Minimize H(x) = 1 x 2 + 36/(1+x) over x > -1.数学困难derivation未尝试免费1960Derive the Optimizer for an Exponential Asymmetry Objective 15For A>0 and B>0, derive the unique minimizer of J(x)=A e x + B e -2x .数学困难derivation未尝试免费1961Exponential Imbalance Optimizer 16A smooth response score is J(x)=e x + 4 e -2x . What x minimizes J?数学简单数值题未尝试免费1962Balanced Exponential Penalties 17A desk minimizes J(x)=6 e x + 3 e -2x . What x is optimal?数学中等derivation未尝试免费1963How the Exponential Optimum Moves With the Back-End Penalty 18For J(x)=A e x + B e -2x , suppose A stays fixed and B is quadrupled. How does the optimizer x* move?数学中等derivation未尝试免费1964Negative Exponential Tilt 19Minimize J(x)=16 e x + 4 e -2x . What x minimizes J?数学困难derivation未尝试免费1965Derive the Optimizer for a Linear-Softplus Objective 20For 0<m<n, derive the unique maximizer of K(x)=m x - n ln(1+e x).数学困难derivation未尝试免费