On Computations in Renewal Risk Models—Analytical and Statistical Aspects

Autor:	Josef Anton Strini, Stefan Thonhauser
Jazyk:	angličtina
Rok vydání:	2020
Předmět:	risk theory renewal model gerber-shiu functions pides Insurance HG8011-9999
Zdroj:	Risks, Vol 8, Iss 1, p 24 (2020)
Druh dokumentu:	article
ISSN:	2227-9091
DOI:	10.3390/risks8010024
Popis:	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.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/8d5d8212ac4247ea98750118af0723c9 Zobrazit plný text záznamu View record in DOAJ Plný text ve formátu PDF Plný text ve formátu HTML
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