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Bayesian estimation for the Markov-modulated diffusion risk model. (English) Zbl 1436.62486

Antoniano-Villalobos, Isadora (ed.) et al., Selected contributions on statistics and data science in Latin America. 33rd “Foro nacional de estadística” (FNE) and 13th “Congreso Latinoamericano de Sociedades de Estadística” (CLATSE), Guadalajara, Mexico, October 1–5, 2018. Cham: Springer. Springer Proc. Math. Stat. 301, 15-31 (2019).
Summary: We consider the Markov-modulated diffusion risk model in which the claim inter-arrivals, claim sizes, premiums, and volatility diffusion process are influenced by an underlying Markov jump process. We propose a method for obtaining the maximum likelihood estimators of its parameters using a Markov chain Monte Carlo algorithm. We present simulation studies to estimate the ruin probability in finite time using the estimators obtained with the method proposed in this paper.
For the entire collection see [Zbl 1427.62003].

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
62M02 Markov processes: hypothesis testing
62M05 Markov processes: estimation; hidden Markov models
60J74 Jump processes on discrete state spaces
91B05 Risk models (general)

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