IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Stochastic processes
A process is observed at all real times t ≥ 0, and at each time it takes one of the values in the finite set {Healthy, Sick, Dead}. How is this stochastic process classified by its time set and state space?
The process is continuous time with a discrete state space. Time can be any real number t ≥ 0, while the process only takes values in the finite set of three states, as in a standard health-sickness-death model.
- ADiscrete time, discrete state space
- BDiscrete time, continuous state space
- CContinuous time, continuous state space
- DContinuous time, discrete state spaceCorrect
- Continuous time, with a state space that is uncountably infinite
Explanation
The time index t takes any non-negative real value, so time is continuous. The states form a finite list, so the state space is discrete. Hence it is a continuous-time, discrete-state process, as in a multiple-state health model.
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