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Economics - Research Publications
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ItemOn the expected discounted penalty function at ruin of a surplus process with interestCai, Jun ; Dickson, David C.M. ( 2001-11)In this paper, we study the expected value of a discounted penalty function at ruin of the classical surplus process modified by the inclusion of interest of the surplus. The 'penalty' is simply a function of the surplus immediately prior to ruin and the deficit at ruin. An integral equation for the expected value is derived, while the exact solution is given when the initial surplus is zero. Dickson's (1992) formulae for the distribution of the surplus immediately prior to ruin in the classical surplus process are generalised to our modified surplus process.
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ItemRuin Probabilities with a Markov Chain Interest ModelCai, Jun ; Dickson, David C. M. ( 2002-08)Ruin probabilities in two generalized discrete time risk processes with a Markov chain interest model are studied. Recursive and integrat equations for the ruin probabilities are given. Generalized Lundberg inequalities for the ruin probabilities are derived both by inductive and martingale approaches. The relationships between these inequalities are discussed. A numerical example is given to illustrate these results.