On Computations in Renewal Risk Models—Analytical and Statistical Aspects

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Abstract

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
JournalRisks
Volume8
Issue number1
DOIs
Publication statusPublished - 4 Mar 2020

ASJC Scopus subject areas

  • Statistics and Probability

Fields of Expertise

  • Information, Communication & Computing

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