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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.13813 |
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Table of Contents:
- In this paper, we first define the multivariate tempered space-fractional Poisson process (MTSFPP) by time-changing the multivariate Poisson process with an independent tempered α-stable subordinator. Its distributional properties, the mixture tempered time and space variants and their PDEs connections are studied. Then we define the multivariate tempered space-fractional negative binomial process (MTSFNBP) and explore its key features. The Lévy measure density for the MTSFNBP is also derived. We present a bivariate risk model with a common shock driven by the tempered space-fractional negative binomial process. We demonstrate that the total claim amount process is stochastically equivalent to a univariate generalized Cramer-Lundberg risk model. In addition, some important ruin measures such as ruin probability, joint distribution of time to ruin and deficit at ruin along with governing integro-differential equations are obtained. Finally we show that the underlying risk process exhibits the long range dependence property.