Problem bank

Problem 283 of 333EasyLinear AlgebraP283

Pushing a regime model forward

  1. A desk models each day as Calm or Stressed, with transition matrix (rows are today's state, columns are tomorrow's)

    P=(0.90.10.30.7)P = \begin{pmatrix} 0.9 & 0.1 \\ 0.3 & 0.7 \end{pmatrix}

    Today the model gives Calm probability 0.8. A strategy makes $2k on a Calm day and loses $5k on a Stressed day.

    (a) What is the regime distribution two days from now?

    (b) Compute PfPf where f=(2,−5)Tf = (2, -5)^T. What does each entry mean?

    (c) Find the expected P&L two days from now in two different ways, and explain why they agree.

    (d) A colleague computes PπTP\pi^T with π=(0.8,0.2)\pi = (0.8, 0.2). What went wrong?