Principles of Actuarial Modeling
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Markov Jump Processes

Worked Example

Consider the following multiple state model in which S(t), the state occupied at time t by a life initially aged x, is assumed to follow a continuous time Markov Jump Process.

Continuous time markov jump process

Let formula 1denote the force of transition at age formula 2 from state i to state j, and let formula 3.

  • Derive the forward Kolmogorov equation:
    formula 4
  • Write down the forward Kolmogorov equations for formula 5

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