Martingale Property Check

Problem

A payoff vector x is a martingale for a Markov chain when E[x_next | state i] = x[i], that is when the sum over j of matrix[i][j] * x[j] equals x[i] for every state i. Return True when all states satisfy this within 1e-9. Return False for malformed input.

Hint

Check that the transition matrix applied to the payoff vector reproduces the vector.

Test cases

case 1

in: [[[0.5,0.5],[0.5,0.5]],[1,1]]

expected: true

case 2

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

expected: false

case 3

in: [[[1,0],[0,1]],[3,7]]

expected: true

case 4

in: [[[0.25,0.75],[0.75,0.25]],[0,0]]

expected: true

case 5

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

expected: false

Starter codePython

def martingale_property_check(matrix, payoff):
    # Your code here
    pass

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