A reinsurance policy provides cover in respect of a single occurrence of a Specified catastrophic event. If such an event occurs, future cover is suspended. However, if a reinstatement premium is paid within one time period of occurrence of the event then the insurance coverage is reinstated. If a second specified event occurs it is not permitted to reinstate the cover and the policy will lapse. The transition rate for the hazard of the specified event is a constant 0.1. Whilst policies are eligible for reinstatement, the transition rate for resumption of cover through paying a reinstatement premium is 0.05. (i) Explain why a model with state space {Cover In Force, Suspended, Lapsed} does not possess the Markov property. (ii) Suggest, giving reasons, additional state(s) such that the expanded system would possess the Markov property. (iii) Sketch a transition diagram for the expanded system. (iv) Write down the transition matrix