Statistical Inference for Partially Observed Markov-Modulated Diffusion Risk Model

F. Baltazar-Larios () and Luz Judith R. Esparza
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F. Baltazar-Larios: Universidad Nacional Autónoma de México
Luz Judith R. Esparza: Universidad Autónoma de Aguascalientes

Methodology and Computing in Applied Probability, 2022, vol. 24, issue 2, 571-593

Abstract: Abstract We propose a method for obtaining the maximum likelihood estimators of the parameters of the Markov-Modulated Diffusion Risk Model in which the inter-claim times, the claim sizes, and the volatility diffusion process are influenced by an underlying Markov jump process. We consider cases when this process has been observed in two scenarios: first, only observing the inter-claim times and the claim sizes in an interval time, and second, considering the number of claims and the underlying Markov jump process at discrete times. In both cases, the data can be viewed as incomplete observations of a model with a tractable likelihood function, so we propose to use algorithms based on stochastic Expectation-Maximization algorithms to do the statistical inference. For the second scenario, we present a simulation study to estimate the ruin probability. Moreover, we apply the Markov-Modulated Diffusion Risk Model to fit a real dataset of motor insurance.

Keywords: Markov-Modulated Diffusion Risk Model; Ruin Probability; Stochastic EM algorithm; Maximum likelihood estimation; 60J60; 60J74; 62P05 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11009-022-09932-7

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