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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.
Original language | English |
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Article number | 24 |
Journal | Risks |
Volume | 8 |
Issue number | 1 |
DOIs | |
Publication status | Published - 4 Mar 2020 |
Keywords
- Gerber-shiu functions
- PIDEs
- Renewal model
- Risk theory
ASJC Scopus subject areas
- Statistics and Probability
- Accounting
- Economics, Econometrics and Finance (miscellaneous)
- Strategy and Management
Fields of Expertise
- Information, Communication & Computing
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Dive into the research topics of 'On Computations in Renewal Risk Models—Analytical and Statistical Aspects'. Together they form a unique fingerprint.Activities
- 2 Talk at conference or symposium
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Approximation of Gerber-Shiu functions
Josef Anton Strini (Speaker)
28 Sept 2021Activity: Talk or presentation › Talk at conference or symposium › Science to science
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Computing Gerber-Shiu functions in renewal risk models
Josef Anton Strini (Speaker)
10 Sept 2020Activity: Talk or presentation › Talk at conference or symposium › Science to science