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Gerber-Shiu Function for a Class of Markov-Modulated Lévy Risk Processes with Two-Sided Jumps

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Abstract

We investigate the Gerber-Shiu discounted penalty function for Markov-modulated Lévy risk processes with random incomes. Firstly, we consider the case when the downward and upward jumps (respectively, claims and random gains) are given by independent compound Poisson processes, with claim sizes with a general distribution function and gains in such a way that their distribution has a rational Laplace transform. Afterwards, we use the above results and weak convergence techniques to study the case when the claims are given by a subordinator and, subsequently, we establish results when the claims are governed by a pure spectrally positive Lévy jump process. Some numerical examples are presented in order to illustrate our results.

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Acknowledgements

The first author thanks financial support from SEP, Grant UGTO-PTC-653. The third author acknowledges the hospitality and financial support of the University of Guanajuato.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad de Guanajuato, Guanajuato, Guanajuato, México

    Ehyter Matías Martín-González & Antonio Murillo-Salas

  2. Facultad de Matemáticas, Universidad Autónoma de Yucatán, Anillo Periférico Norte, Tablaje Cat. 13615, Colonia Chuburná Hidalgo Inn, Mérida, Yucatán, México

    Henry Pantí

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  1. Ehyter Matías Martín-González
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  2. Antonio Murillo-Salas
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  3. Henry Pantí
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Correspondence to Antonio Murillo-Salas.

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Martín-González, E.M., Murillo-Salas, A. & Pantí, H. Gerber-Shiu Function for a Class of Markov-Modulated Lévy Risk Processes with Two-Sided Jumps. Methodol Comput Appl Probab 24, 2779–2800 (2022). https://doi.org/10.1007/s11009-022-09954-1

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  • DOI: https://doi.org/10.1007/s11009-022-09954-1

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