NSCPHD1076 Statistical inferens for Markov processes
PhD programme in Actuarial Mathematics
PhD programme in Statistics
PhD programme in Probabilty Theory
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The course will focus on statistical inferens and estimation of Markov processes. We will consider the following processes: Markov chains, fully observed Markov jump process, discretely observed Markov jump processes and discretely observed diffusions. While the estimation in the fully observed models is relatively easy and linked to methods for multinomial distributions, the estimation of the discretely observed processes is more involved. Here we shall make use of incomplete data methods like the EM algortihm and Markov chain Monte Carlo methods. Markovian bridges play an important role and both explicit methods and simulation will be exploited. The explicit methods calculates conditional expectations of sufficient statistics using Markov chain theory.
The methods will be applied to financial data from credit risk modeling (discretely observed Markov jump processes), stock prices (discretely observed diffusions) and ruin probability estimation (insurance risk) using estimation of phase--type distributions and Markov chain Monte Carlo.
Necessary background on Markov processes and incomplete data methods will be provided as an integrated part of the course.
At the end of the course the student is expected to have:
Knowledge about inference for Markov processes, fully or discretely observed, Markov bridges and incomplete data methods in the context.
Skills: At the end of the course the student is expected to be
follow and reproduce arguments at a high abstract level corresponding to
the contents of the course.
Competences in the contents of the course.
- 7,5 ECTS
- Type of assessment
- Oral examination, 30 min30 min preparation
- All aids allowed
- Marking scale
- passed/not passed
- Censorship form
- No external censorship
Same as ordinary.
Criteria for exam assesment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.