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Quantitative Finance

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  • $\begingroup$ Hi, what are your thoughts on this problem? $\endgroup$ Commented Oct 1, 2024 at 12:46
  • $\begingroup$ I though the solution is $\mathbb{E}_t[\lambda_T]=\lambda_He^{-\mu_H(T-t)}+\lambda_L(1-e^{-\mu_H(T-t)})$, assuming $\lambda_t=\lambda_H$. Is that correct? $\endgroup$ Commented Oct 1, 2024 at 14:19
  • $\begingroup$ I believe the long run fractions of time spent in the two states are $\frac{\mu_L}{\mu_L+\mu_H},\frac{\mu_H}{\mu_L+\mu_H}$. For ex when the transition rates are equal you spend 50% of the time in each state. $\endgroup$ Commented Oct 1, 2024 at 18:20
  • $\begingroup$ that makes sense. $\endgroup$ Commented Oct 1, 2024 at 19:20