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FROM RUIN TO BANKRUPTCY FOR COMPOUND POISSON SURPLUS PROCESSES

Published online by Cambridge University Press:  18 June 2013

Hansjörg Albrecher  and
Volkmar Lautscham
Hansjörg Albrecher
Affiliation:
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
Volkmar Lautscham*
Affiliation:
Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne, UNIL-Dorigny, CH-1015 Lausanne, Switzerland
*
E-Mail: volkmar.lautscham@unil.ch
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Abstract

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.

Keywords

Classical risk processOmega modelruin probabilitydiscounted penalty functionbankruptcy rate function
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 43 , Issue 2 , May 2013 , pp. 213 - 243
Copyright
Copyright © ASTIN Bulletin 2013 

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