×

zbMATH — the first resource for mathematics

The adjustment function in ruin estimates under interest force. (English) Zbl 0910.62107
Summary: We continue our discussion of infinite time ruin probabilities in continuous time in a compound Poisson process with a constant premium rate and a constant interest force. Using appropriate conditions the ruin probability is exponentially bounded. The usual adjustment coefficient is replaced by an adjustment function depending in an intricate way on the initial reserve, the interest force and all ingredients of the compound Poisson process. After deriving general bounds we also give expansions for the case where the interest force is small.

MSC:
62P05 Applications of statistics to actuarial sciences and financial mathematics
91B30 Risk theory, insurance (MSC2010)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Embrechts, P.; Jensen, J.L.; Maejima, M.; Teugels, J.L., Approximations for compound Poisson and Pólya processes, Advances in applied probability, 17, 623-637, (1985) · Zbl 0576.62098
[2] Knuth, D.E., ()
[3] Sundt, B.; Teugels, J.L., Ruin estimates under interest force, Insurance: mathematics and economics, 16, 7-22, (1995) · Zbl 0838.62098
[4] Teugels, J.L.; Willmot, G., Approximations for stop-loss premiums, Insurance: mathematics and economics, 6, 195-202, (1987) · Zbl 0624.62097
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.