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On Computations in Renewal Risk Models—Analytical and Statistical Aspects

Graz University of Technology, Institute of Statistics, Kopernikusgasse 24/III, A-8010 Graz, Austria
Author to whom correspondence should be addressed.
Risks 2020, 8(1), 24;
Received: 13 December 2019 / Revised: 24 February 2020 / Accepted: 28 February 2020 / Published: 4 March 2020
(This article belongs to the Special Issue Loss Models: From Theory to Applications)
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. View Full-Text
Keywords: risk theory; renewal model; gerber-shiu functions; PIDEs risk theory; renewal model; gerber-shiu functions; PIDEs
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Strini, J.A.; Thonhauser, S. On Computations in Renewal Risk Models—Analytical and Statistical Aspects. Risks 2020, 8, 24.

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