On Computations in Renewal Risk Models—Analytical and Statistical Aspects

Josef Anton Strini and Stefan Thonhauser
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Josef Anton Strini: Graz University of Technology, Institute of Statistics, Kopernikusgasse 24/III, A-8010 Graz, Austria
Stefan Thonhauser: Graz University of Technology, Institute of Statistics, Kopernikusgasse 24/III, A-8010 Graz, Austria

Risks, 2020, vol. 8, issue 1, 1-20

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.

Keywords: risk theory; renewal model; gerber-shiu functions; PIDEs (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:gam:jrisks:v:8:y:2020:i:1:p:24-:d:328516

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