IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Stochastic processes
Which of the following processes is a Markov process in continuous time with a discrete state space?
The Poisson claim-count process is a continuous-time Markov process with a discrete state space. It is observed at all times t, takes values 0, 1, 2 and so on, and its future depends only on the current count.
- AThe Poisson process counting claims, N_tCorrect
- BBrownian motion, B_t
- CA stationary AR(1) series observed monthly
- DThe running maximum of a daily share price index
- Cumulative rainfall measured at the end of each year
Explanation
The Poisson process has continuous time and takes integer values, so its state space is discrete, and its future depends only on the current count. Brownian motion has a continuous state space. The AR(1) series and annual rainfall are discrete time.
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