CVaR Linearization

Problem

Evaluate the Rockafellar-Uryasev CVaR linearization at a given threshold.

Return v + sum(max(0, loss - v)) / (alpha * n), where v is the VaR candidate, alpha the tail level, and n the number of scenarios. Minimizing this over v yields the CVaR.

Hint

Only losses above the threshold contribute to the tail average.

Test cases

case 1

in: [[1,2,3,4],2,0.5]

expected: 3.5

case 2

in: [[0.5,1,1.5],1,0.25]

expected: 1.6666666666666665

case 3

in: [[2,2],2,0.5]

expected: 2

Starter codePython

def cvar_linearized(losses, v, alpha):
    # Your code here
    pass

3 test cases · run your code against them in the editor