×

zbMATH — the first resource for mathematics

The effect of interest on negative surplus. (English) Zbl 0894.90045
Summary: In the classical continuous time surplus process, we allow the process to continue if the surplus falls below zero. When the surplus is below zero, we assume that the insurer borrows any sum of money required to pay claims, and pays interest on this borrowing. We use simulation to study moments and distributions of three quantities: the time to recovery to surplus level zero, the number of claims that occur when the surplus is below zero, and the maximum absolute value of the surplus process when it is below zero. We also show how simulation can be used to estimate the probability of absolute ruin.

MSC:
91B30 Risk theory, insurance (MSC2010)
Software:
S-PLUS
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bowers, N.L.; Gerber, H.U.; Hickman, J.C.; Jones, D.A.; Nesbitt, C.J., Actuarial mathematics, (1986), Society of Actuaries Itasca, IL · Zbl 0634.62107
[2] Dassios, A.; Embrechts, P., Martingales and insurance risk, Communications in statistics - stochastic models, 5, 181-217, (1989) · Zbl 0676.62083
[3] Dickson, D.C.M., Approximate calculation of moments of ruin related distributions, (), 103-110
[4] Dickson, D.C.M.; Egídio dos Reis, A.D., On the distribution of the duration of negative surplus, Scandinavian actuarial journal, 148-164, (1996) · Zbl 0864.62069
[5] Dickson, D.C.M.; Egídio dos Reis, A.D.; Waters, H.R., Some stable algorithms in ruin theory and their applications, ASTIN bulletin, 25, 153-175, (1995)
[6] Egídio dos Reis, A.D., How long is the surplus below zero?, Insurance: mathematics and economics, 12, 23-38, (1993) · Zbl 0777.62096
[7] Gerber, H.U., When does the surplus reach a given target?, Insurance: mathematics and economics, 9, 115-119, (1990) · Zbl 0731.62153
[8] Picard, P., On some measures of the severity of ruin in the classical Poisson model, Insurance: mathematics and economics, 14, 107-115, (1994) · Zbl 0813.62093
[9] ()
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.