On Computations in Renewal Risk Models—Analytical and Statistical Aspects

Josef Anton Strini, Stefan Thonhauser*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We discuss aspects of numerical methods for the computation of Gerber-Shiu or discounted penalty-functions in renewal risk models. We take an analytical point of view and link this function to a partial-integro-differential equation and propose a numerical method for its solution. We show weak convergence of an approximating sequence of piecewise-deterministic Markov processes (PDMPs) for deriving the convergence of the procedures. We will use estimated PDMP characteristics in a subsequent step from simulated sample data and study its effect on the numerically computed Gerber-Shiu functions. It can be seen that the main source of instability stems from the hazard rate estimator. Interestingly, results obtained using MC methods are hardly affected by estimation.
Original languageEnglish
Article number24
Issue number1
Publication statusPublished - 4 Mar 2020


  • Gerber-shiu functions
  • PIDEs
  • Renewal model
  • Risk theory

ASJC Scopus subject areas

  • Statistics and Probability
  • Accounting
  • Economics, Econometrics and Finance (miscellaneous)
  • Strategy and Management

Fields of Expertise

  • Information, Communication & Computing


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