Title :
Filtering a Markov Modulated Random Measure
Author :
Elliott, Robert J. ; Siu, Tak Kuen ; Yang, Hailiang
Author_Institution :
Haskayne Sch. of Bus., Univ. of Calgary, Calgary, AB, Canada
Abstract :
We develop a new exact filter when a hidden Markov chain influences both the sizes and times of a marked point process. An example would be an insurance claims process, where we assume that both the stochastic intensity of the claim arrivals and the distribution of the claim sizes depend on the states of an economy. We also develop the robust filter-based and smoother-based EM algorithms for the on-line recursive estimates of the unknown parameters in the Markov-modulated random measure. Our development is in the framework of modern theory of stochastic processes.
Keywords :
expectation-maximisation algorithm; filtering theory; hidden Markov models; insurance; recursive estimation; stochastic processes; Markov modulated random measure; hidden Markov chain; insurance claims process; online recursive estimation; robust filter-based EM algorithms; smoother-based EM algorithms; stochastic intensity; stochastic processes; Environmental economics; Filtering; Filters; Helium; Hidden Markov models; Insurance; Measurement uncertainty; Recursive estimation; Robustness; Stochastic processes; Insurance risk models; Markov-modulated random measures; martingales; model uncertainty; reference probability; robust EM algorithms;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2009.2034227
