Continuous-Time Markov Jump Processes

Construct the generator matrix for a continuous-time Markov jump process from given transition rates.

Calculate holding time distributions for each state in a Markov jump process.

Set up and solve Kolmogorov's forward and backward equations for multi-state actuarial models.

Compute transition probabilities from a generator matrix using matrix exponentiation.

Define and calculate the expected present value of state-contingent cash flows.

Calculate net premiums and policy reserves for multi-state insurance products using expected present values.