Surplus Analysis of Sparre Andersen Insurance Risk Processes
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Beschreibung
This carefully written monograph covers the Sparre Andersen process in an actuarial context using the renewal process as the model for claim counts.
A unified reference on Sparre Andersen (renewal risk) processes is included, often missing from existing literature. The authors explore recent results and analyse various risk theoretic quantities associated with the event of ruin, including the time of ruin and the deficit of ruin. Particular attention is given to the explicit identification of defective renewal equation components, which are needed to analyse various risk theoretic quantities and are also relevant in other subject areas of applied probability such as dams and storage processes, as well as queuing theory.
Aimed at researchers interested in risk/ruin theory and related areas, this work will also appeal to graduate students in classical and modern risk theory and Gerber-Shiu analysis.
This carefully written monograph covers the Sparre Andersen process in an actuarial context using the renewal process as the model for claim counts.
A unified reference on Sparre Andersen (renewal risk) processes is included, often missing from existing literature. The authors explore recent results and analyse various risk theoretic quantities associated with the event of ruin, including the time of ruin and the deficit of ruin. Particular attention is given to the explicit identification of defective renewal equation components, which are needed to analyse various risk theoretic quantities and are also relevant in other subject areas of applied probability such as dams and storage processes, as well as queuing theory.
Aimed at researchers interested in risk/ruin theory and related areas, this work will also appeal to graduate students in classical and modern risk theory and Gerber-Shiu analysis.
Provides a comprehensive treatment of Sparre Andersen risk processes arising from models in actuarial science Offers an in-depth analysis of standard models, with a rigorous mathematical presentation Presents ideas and techniques that may be adapted to other models as appropriate Explores dependence features, such as claim size and interclaim time Includes supplementary material: sn.pub/extras
Autor*in
Gordon E. Willmot
Themen in »Surplus Analysis of Sparre Andersen Insurance Risk Processes«
MSC (2010): 60-02, 60G50, 60K10, 62P05 dependent Sparre Andersen risk model classical compound poisson risk model classical Poisson risk model derivation classical Poisson risk model analysis Gerber Shiu function ruin probability deficit at ruin time of ruin mixed Erlang distribution defective renewal equation renewal risk process Laplace transform Dickson Hipp operator delayed renewal risk model
Stimmen zu »Surplus Analysis of Sparre Andersen Insurance Risk Processes«
“The monograph is devoted to the surplus analysis of the Sparre-Andersen process using the renewal process as the model for claim counts. … This book is intended for researchers interested in ruin/risk theory, and will also be useful for graduate students specialized in classical and modern risk theory.” (Anatoliy Swishchuk, zbMATH 1391.91006, 2018)
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