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From ruin to bankruptcy for compound Poisson surplus processes. (English) Zbl 1283.91084
Within risk theory, the study focuses on a relaxation of the ruin concept to the bankruptcy concept: the insurance company has a positive surplus-dependent probability to continue the insurance activity also in the case of temporary negative surplus.
In the first part of the paper equations involving the probability of bankruptcy are derived and explicit solutions are calculated for some particular bankruptcy rate functions and exponential claim sizes. Under more general hypotheses on bankruptcy rate functions, solutions are derived by means of suitable approximating techniques. Then, a simulation approach is presented and tested.
Finally, extensions to the discounted penalty function are analyzed, in order to obtain further risk measures.

MSC:
91B30 Risk theory, insurance (MSC2010)
91G50 Corporate finance (dividends, real options, etc.)
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[1] Scandinavian Actuarial Journal 2 pp 105– (2004)
[2] Insurance Risk and Ruin (2005) · Zbl 1060.91078
[3] DOI: 10.1080/15326348908807105 · Zbl 0676.62083 · doi:10.1080/15326348908807105
[4] Ruin Probabilities (2010) · Zbl 1247.91080
[5] Mitteilungen der Schweizerischen Vereinigung der Versicherungsmatematiker 71 pp 63– (1971)
[6] DOI: 10.1007/s13385-011-0006-4 · Zbl 1219.91062 · doi:10.1007/s13385-011-0006-4
[7] ASTIN Bulletin 41 pp 645– (2011)
[8] Handbook of Mathematical Functions, Applied Mathematics Series 55 (1972)
[9] DOI: 10.1016/j.spa.2011.07.008 · Zbl 1227.60061 · doi:10.1016/j.spa.2011.07.008
[10] DOI: 10.1017/S0021900200004721 · doi:10.1017/S0021900200004721
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