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Erscheinungsjahr: 
2020
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[Journal:] Risks [ISSN:] 2227-9091 [Volume:] 8 [Issue:] 1 [Article No.:] 24 [Publisher:] MDPI [Place:] Basel [Year:] 2020 [Pages:] 1-20
Verlag: 
MDPI, Basel
Zusammenfassung: 
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.
Schlagwörter: 
gerber-shiu functions
PIDEs
renewal model
risk theory
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