CEMAPRE Seminar

Dividends and ruin problems in finite time

Rui M. R. Cardoso
(CMA and Departamento de Matemática, FCT-UNL)

Abstract: In this work we consider three different classical risk models modified by the introduction of a constant dividend barrier, that is, when the surplus exceeds this threshold the insurer pays dividends to shareholders. For our first model the dividend rate is equal to the premium income, the so called dividend barrier strategy. We derive the finite time version of recursions due to Dickson and Waters [Dickson, D. C. M. and Waters, H. R. (2004). Some optimal dividends problems. Astin Bulletin, 34(1):49--74] and we present a numerical procedure based on the Markov chain approach (Cardoso and Egídio dos Reis [Cardoso, R. M. R. and Egídio dos Reis, A. D. (2002). Recursive calculation of time to ruin distributions. Insurance: Mathematics and Economics, 30(2):219--230] and Cardoso and Waters [Cardoso, R. M. R. and Waters, H. R. (2003). Recursive calculation of finite time ruin probabilities under interest force. Insurance: Mathematics and Economics, 33(3):659--676; Cardoso, R. M. R. and Waters, H. R. (2005). Calculation of finite time ruin probabilities for some risk models. Insurance: Mathematics and Economics, 37(2):197--215]) for the calculation of the expected discounted value of dividend payouts, until ruin occurs or up to time t, and its net value when shareholders provide the initial surplus and pay the deficit at ruin. Also, using the Markov chain approach, we produce bounds for the former expected value. We extend this risk model by allowing the process to continue after ruin, the second risk model analysed in this paper and introduced by Dickson and Waters [Dickson, D. C. M. and Waters, H. R. (2004). Some optimal dividends problems. Astin Bulletin, 34(1):49--74]. The Markov chain approach is again used to obtain approximations to the net expected present value of dividends paid. A threshold dividend strategy is also covered under which the dividend rate is lower than the premium rate. For this risk model we present bounds for the expected present value of dividend payments. We also present numerical algorithms for the calculation of the finite time ruin probability.

Friday, April 11, 2008
Time: 15h30
Room: Sala CTT, Edificio Quelhas, ISEG
http://cemapre.iseg.ulisboa.pt/seminars/cemapre/