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FROM RUIN TO BANKRUPTCY FOR COMPOUND POISSON SURPLUS PROCESSES

Albrecher, Hansjörg ; Lautscham, Volkmar

In: ASTIN Bulletin, 2013, vol. 43, no. 2, p. 213-243

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    Titre
    • FROM RUIN TO BANKRUPTCY FOR COMPOUND POISSON SURPLUS PROCESSES
    Auteur
    • Albrecher, Hansjörg. Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne, UNIL-Dorigny, CH-1015 Lausanne, and Swiss Finance Institute, Switzerland E-Mail: hansjoerg.albrecher@unil.ch
    • Lautscham, Volkmar. Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne, UNIL-Dorigny, CH-1015 Lausanne, Switzerland
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • ASTIN Bulletin, 2013, vol. 43, no. 2, p. 213-243. Cambridge University Press
    Autre version électronique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:302875
    Summary
    In classical risk theory, the infinite-time ruin probability of a surplus process Ct is calculated as the probability of the process becoming negative at some point in time. In this paper, we consider a relaxation of the ruin concept to the concept of bankruptcy, according to which one has a positive surplus-dependent probability to continue despite temporary negative surplus. We study the resulting bankruptcy probability for the compound Poisson risk model with exponential claim sizes for different bankruptcy rate functions, deriving analytical results, upper and lower bounds as well as an efficient simulation method. Numerical examples are given and the results are compared with the classical ruin probabilities. Finally, it is illustrated how the analysis can be extended to study the discounted penalty function under this relaxed ruin criterion