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Ruin theory in a hidden Markov-modulated risk model. (English) Zbl 1237.91127
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.
MSC:
91B30Risk theory, insurance
93E11Filtering in stochastic control
60J20Applications of Markov chains and discrete-time Markov processes on general state spaces