## Conditional tail expectations for multivariate phase-type distributions.(English)Zbl 1079.62022

Summary: The conditional tail expectation in risk analysis describes the expected amount of risk that can be experienced given that a potential risk exceeds a threshold value, and provides an important measure of right-tail risk. We study the convolution and extreme values of dependent risks that follow a multivariate phase-type distribution, and derive explicit formulae for several conditional tail expectations of the convolution and extreme values for such dependent risks. Utilizing the underlying Markovian property of these distributions, our method not only provides structural insight, but also yields some new distributional properties of multivariate phase-type distributions.

### MSC:

 62E15 Exact distribution theory in statistics 62P05 Applications of statistics to actuarial sciences and financial mathematics 91B30 Risk theory, insurance (MSC2010) 60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) 62N05 Reliability and life testing
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### References:

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