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Ruin analysis of a threshold strategy in a discrete-time Sparre Andersen model. (English) Zbl 1245.91043
Summary: We extend the methodology of Alfa and Drekic [A. S. Alfa and S. Drekic, Astin Bull. 37, No. 2, 293–317 (2007; Zbl 1154.62076)] to analyze a discrete-time, delayed Sparre Andersen insurance risk model featuring a single threshold level and randomized dividend payments. Using matrix analytic techniques, we construct a set of computational procedures enabling one to calculate probability distributions associated with fundamental ruin-related quantities of interest, namely the time of ruin, the surplus immediately prior to ruin, and the deficit at ruin. Special cases of the general model, including the ordinary and stationary Sparre Andersen variants, are examined in several numerical examples.

91B30 Risk theory, insurance (MSC2010)
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60J22 Computational methods in Markov chains
Full Text: DOI
[1] Alfa AS (2004) Markov chain representations of discrete distributions applied to queueing models. Comput Oper Res 31:2365–2385 · Zbl 1067.90158 · doi:10.1016/S0305-0548(03)00192-8
[2] Alfa AS, Drekic S (2007) Algorithmic analysis of the Sparre Andersen model in discrete time. ASTIN Bull 37:293–317 · Zbl 1154.62076 · doi:10.2143/AST.37.2.2024068
[3] Bao Z (2007) A note on the compound binomial model with randomized dividend strategy. Appl Math Comput 194:276–286 · Zbl 1193.91062 · doi:10.1016/j.amc.2007.04.023
[4] Cossette H, Landriault D, Marceau E (2006) Ruin probabilities in the discrete time renewal risk model. Insurance Math Econ 38:309–323 · Zbl 1090.60076 · doi:10.1016/j.insmatheco.2005.09.005
[5] Dickson DCM, Waters H (2004) Some optimal dividends problems. ASTIN Bull 34:49–74 · Zbl 1097.91040 · doi:10.2143/AST.34.1.504954
[6] Karlin S, Taylor HM (1975) A first course in stochastic processes, 2nd edn. Academic, New York · Zbl 0315.60016
[7] Kim B, Kim H-S, Kim J (2008) A risk model with paying dividends and random environment. Insurance Math Econ 42:717–726 · Zbl 1152.91589 · doi:10.1016/j.insmatheco.2007.08.001
[8] Landriault D (2008) Randomized dividends in the compound binomial model with a general premium rate. Scand Actuar J 2008:1–15 · Zbl 1164.91032 · doi:10.1080/03461230701642489
[9] Tan J, Yang X (2006) The compound binomial model with randomized decisions on paying dividends. Insurance Math Econ 39:1–18 · Zbl 1147.91349 · doi:10.1016/j.insmatheco.2006.01.001
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