an:05961812
Zbl 1237.91127
Elliott, Robert J.; Siu, Tak Kuen; Yang, Hailiang
Ruin theory in a hidden Markov-modulated risk model
EN
Stoch. Models 27, No. 3, 474-489 (2011).
00285838
2011
j
91B30 93E11 60J20
Dirichlet problem; filtering; hidden Markovian regime-switching model; innovations approach; partial differential equation; ruin probability
Summary: We discuss ruin theory when the insurance risk process is described by a hidden Markov, regime-switching diffusion process. The innovations approach to filtering theory is used to transform the partially observed modeling framework into one with complete observations. (Robust) filters for the hidden states of the chain are given. A partial differential equation for the ruin probability is derived in the ``filtered'' model.