Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/257979 
Year of Publication: 
2020
Citation: 
[Journal:] Risks [ISSN:] 2227-9091 [Volume:] 8 [Issue:] 1 [Article No.:] 24 [Publisher:] MDPI [Place:] Basel [Year:] 2020 [Pages:] 1-20
Publisher: 
MDPI, Basel
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.
Subjects: 
gerber-shiu functions
PIDEs
renewal model
risk theory
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
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