Analysis of a Multivariate Claim Process

Qi-Ming He () and Jiandong Ren
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Qi-Ming He: University of Waterloo
Jiandong Ren: University of Western Ontario

Methodology and Computing in Applied Probability, 2016, vol. 18, issue 1, 257-273

Abstract: Abstract The first part of this paper introduces a class of discrete multivariate phase-type (MPH) distributions. Recursive formulas are found for joint probabilities. Explicit expressions are obtained for means, variances and co-variances. The discrete MPH-distributions are used in the second part of the paper to study multivariate insurance claim processes in risk analysis, where claims may arrive in batches, the arrivals of different types of batches may be correlated and the amounts of different types of claims in a batch may be dependent. Under certain conditions, it is shown that the total amounts of claims accumulated in some random time horizon are discrete MPH random vectors. Matrix-representations of the discrete MPH-distributions are constructed explicitly. Efficient computational methods are developed for computing risk measures of the total claims of different types of claim batches and individual types of claims (e.g., joint distribution, mean, variance, correlation and value at risk.)

Keywords: Matrix-analytic methods; Risk analysis; Markovian arrival process; Multivariate phase-type distribution; 60K (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11009-014-9420-9

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