×

zbMATH — the first resource for mathematics

On the discounted penalty function in a discrete time renewal risk model with general interclaim times. (English) Zbl 1224.91094
A discrete time Sparre Andersen risk model with an arbitrary interclaim times distribution is considered and some general analytic properties of the expected discounted penalty (Gerber-Shiu) function \(\phi_v(u)\) are explored. It is shown that \(\phi_v(u)\) satisfies a recursive formula. An explicit expression for \(\phi_v(u)\) is derived in terms of a compound geometric distribution function for general penalty function. In particular, constant claim amounts and mixed geometric claim amounts are studied.

MSC:
91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Cheng S., Insurance: Mathematics and Economics 26 pp 239– (2000) · Zbl 1013.91063 · doi:10.1016/S0167-6687(99)00053-0
[2] Landriault D., Insurance: Mathematics and Economics 42 pp 600– (2008) · Zbl 1152.91591 · doi:10.1016/j.insmatheco.2007.06.004
[3] Li S., Scandinavian Actuarial Journal 4 pp 241– (2005) · Zbl 1142.91043 · doi:10.1080/03461230510009745
[4] Li S., Scandinavian Actuarial Journal 4 pp 271– (2005) · Zbl 1143.91033 · doi:10.1080/03461230510009808
[5] Li S., Advances in Applied Probability 37 pp 836– (2005) · Zbl 1077.60063 · doi:10.1239/aap/1127483750
[6] Malinovskii V., Insurance: Mathematics and Economics 22 pp 123– (1998) · Zbl 0907.90099 · doi:10.1016/S0167-6687(98)80001-2
[7] Pavlova K., Insurance: Mathematics and Economics 2 pp 267– (2004) · Zbl 1103.91046 · doi:10.1016/j.insmatheco.2004.04.006
[8] Wang R., ASTIN Bulletin 32 pp 81– (2002) · Zbl 1098.60515 · doi:10.2143/AST.32.1.1016
[9] Willmot G. E., Insurance: Mathematics and Economics 41 pp 17– (2007) · Zbl 1119.91058 · doi:10.1016/j.insmatheco.2006.08.005
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.