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Abstract
In this paper, we consider discounted penalty functions, also called GerberShiu functions, in a Markovian shotnoise environment. At first, we exploit the underlying structure of piecewisedeterministic Markov processes (PDMPs) to show that these penalty functions solve certain partial integrodifferential equations (PIDEs). Since these equations cannot be solved exactly, we develop a numerical scheme that allows us to determine an approximation of such functions. These numerical solutions can be identified with penalty functions of continuoustime Markov chains with finite state space. Finally, we show the convergence of the corresponding generators over suitable sets of functions to prove that these Markov chains converge weakly against the original PDMP. That gives us that the numerical approximations converge to the discounted penalty functions of the original Markovian shotnoise environment.
Original language  English 

Article number  17 
Journal  Methodology and Computing in Applied Probability 
Volume  25 
DOIs  
Publication status  Published  Mar 2023 
Keywords
 GerberShiu functions
 Markov processes
 Risk theory
 ShotNoise
 Weak convergence
ASJC Scopus subject areas
 Mathematics(all)
 Statistics and Probability
Fields of Expertise
 Information, Communication & Computing
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 1 Active

FWF  Risk Modelling  Analysis, Simulation and Optimization
1/07/20 → 30/06/24
Project: Research project