Dickson, David C. M.; Li, Shuanming Erlang risk models and finite time ruin problems. (English) Zbl 1277.91081 Scand. Actuar. J. 2012, No. 3, 183-202 (2012). Summary: We consider the joint density of the time of ruin and deficit at ruin in the Erlang(\(n\)) risk model. We give a general formula for this joint density and illustrate how the components of this formula can be found in the special case when \(n=2\). We then show how the formula can be implemented numerically for a general value of \(n\). We also discuss how the ideas extend to the generalised Erlang(\(n\)) risk model. Cited in 6 Documents MSC: 91B30 Risk theory, insurance (MSC2010) 60K10 Applications of renewal theory (reliability, demand theory, etc.) Keywords:Erlang risk models; time of ruin; deficit at ruin; joint distribution PDF BibTeX XML Cite \textit{D. C. M. Dickson} and \textit{S. Li}, Scand. Actuar. J. 2012, No. 3, 183--202 (2012; Zbl 1277.91081) Full Text: DOI References: [1] DOI: 10.1017/CBO9780511569609 · Zbl 0592.65093 · doi:10.1017/CBO9780511569609 [2] DOI: 10.1017/S1748499500000348 · doi:10.1017/S1748499500000348 [3] DOI: 10.1016/S0167-6687(01)00091-9 · Zbl 1074.91549 · doi:10.1016/S0167-6687(01)00091-9 [4] DOI: 10.1080/03461230510009853 · Zbl 1144.91025 · doi:10.1080/03461230510009853 [5] DOI: 10.1016/j.insmatheco.2009.05.001 · Zbl 1231.91176 · doi:10.1016/j.insmatheco.2009.05.001 [6] DOI: 10.2143/AST.35.1.583165 · Zbl 1097.62113 · doi:10.2143/AST.35.1.583165 [7] DOI: 10.2143/AST.33.1.1036 · Zbl 1062.60007 · doi:10.2143/AST.33.1.1036 [8] Gerber H. U., North American Actuarial Journal 9 (2) pp 49– (2005) · Zbl 1085.62508 · doi:10.1080/10920277.2005.10596197 [9] Graham R. L., Concrete mathematics, 2. ed. (1994) [10] Landriault D., North American Actuarial Journal 13 (2) pp 252– (2009) · doi:10.1080/10920277.2009.10597550 [11] DOI: 10.1016/j.insmatheco.2004.01.002 · Zbl 1188.91089 · doi:10.1016/j.insmatheco.2004.01.002 [12] Panjer H. H., ASTIN Bulletin 12 pp 22– (1981) · doi:10.1017/S0515036100006796 [13] DOI: 10.1214/aoms/1177704970 · Zbl 0103.13302 · doi:10.1214/aoms/1177704970 [14] DOI: 10.1016/j.spl.2004.12.015 · Zbl 1104.91046 · doi:10.1016/j.spl.2004.12.015 [15] DOI: 10.1016/j.insmatheco.2006.08.005 · Zbl 1119.91058 · doi:10.1016/j.insmatheco.2006.08.005 [16] Willmot G. E., North American Actuarial Journal 11 (2) pp 99– (2007) · doi:10.1080/10920277.2007.10597450 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.