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Abstract
In this paper we suppose that the intensity parameter of the Pólya-Aeppli process is a function of time t and call the resulting process a non-homogeneous Pólya-Aeppli process (NHPAP). The NHPAP can be represented as a compound non-homogeneous Poisson process with geometric compounding distribution as well as a pure birth process. For this process we give two definitions and show their equivalence. Also, we derive some interesting properties of NHPAP and use simulation the illustrate the process for particular intensity functions. In addition, we introduce the standard risk model based on NHPAP, analyze the ruin probability for this model and include an example of the process under exponentially distributed claims.
Acknowledgements
We are thankful to Prof. N.Balakrishnan for his encouragement and useful advice during our study. Also, we are grateful to Victoria University of Wellington for the support provided during the visit of the second author to New Zealand. The research of the second author was partially supported by project DN12/11/20.dec.2017 of Ministry of Education and Science of Bulgaria.