Statistical inferens for Markov processes

Course content

 

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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.  

 

 

 

 

Education

PhD programme in Actuarial Mathematics
PhD programme in Statistics
PhD programme in Probabilty Theory

 

Learning outcome

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 able to 
follow and reproduce arguments at a high abstract level corresponding to 
the contents of the course. 

Competences in the contents of the course.

7 weeks with 4 lectures.

ECTS
7,5 ECTS
Type of assessment
Oral examination, 30 min
30 min preparation
Aid
All aids allowed
Marking scale
passed/not passed
Censorship form
No external censorship
Criteria for exam assessment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.

Single subject courses (day)

  • Category
  • Hours
  • Preparation
  • 178
  • Lectures
  • 28
  • English
  • 206