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

Author

Listed:
  • Ehyter Matías Martín-González

    (Universidad de Guanajuato)

  • Antonio Murillo-Salas

    (Universidad de Guanajuato)

  • Henry Pantí

    (Universidad Autónoma de Yucatán)

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.

Suggested Citation

  • Ehyter Matías Martín-González & Antonio Murillo-Salas & Henry Pantí, 2022. "Gerber-Shiu Function for a Class of Markov-Modulated Lévy Risk Processes with Two-Sided Jumps," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2779-2800, December.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:4:d:10.1007_s11009-022-09954-1
    DOI: 10.1007/s11009-022-09954-1
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    References listed on IDEAS

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