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Economics - Research Publications
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ItemThe maximum surplus before ruin in an Erlang(n) risk process and related problemsLI, S ; DICKSON, D ( 2006)
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ItemOptimal Dividends under a Ruin ProbabilityConstraintDickson, David CM ; Drekic, Steve ( 2005-10)We consider a classical surplus process modified by the paymentof dividends when the insurer’s surplus exceeds a threshold. We use aprobabilistic argument to obtain general expressions for the expected present value of dividend payments, and show how these expressions can be applied for certain individual claim amount distributions. We then consider the question of maximising the expected present valueof dividend payments subject to a constraint on the insurer’s ruin probability.
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ItemOptimal dynamic reinsuranceDickson, David CM ; Waters, Howard R ( 2006-01)We consider a classical surplus process where the insurer can choosea different level of reinsurance at the start of each year. We assume theinsurer’s objective is to minimise the probability of ruin up to somegiven time horizon, either in discrete or continuous time. We developformulae for ruin probabilities under the optimal reinsurance strategy,i.e. the optimal retention each year as the surplus changes andthe period until the time horizon shortens. For our compound Poissonprocess, it is not feasible to evaluate these formulae, and hencedetermine the optimal strategies, in any but the simplest cases. Weshow how we can determine the optimal strategies by approximatingthe (compound Poisson) aggregate claims distributions by translatedgamma distributions, and, alternatively, by approximating the compoundPoisson process by a translated gamma process.
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ItemOn the distribution of the deficit at ruin when claims are phase-typeDrekic, S ; DICKSON, D ; Stanford, DA ; Willmot, GE ( 2005)
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ItemOptimal dynamic reinsuranceDICKSON, D. ; WATERS, H. ( 2006)
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ItemSome Finite Time Ruin ProblemsDickson, DCM (Cambridge University Press (CUP), 2007-09)ABSTRACT In the classical risk model, we use probabilistic arguments to write down expressions in terms of the density function of aggregate claims for joint density functions involving the time to ruin, the deficit at ruin and the surplus prior to ruin. We give some applications of these formulae in the cases when the individual claim amount distribution is exponential and Erlang(2).
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ItemOptimal Dividends Under a Ruin Probability ConstraintDickson, DCM ; Drekic, S (Cambridge University Press (CUP), 2006-09)ABSTRACT We consider a classical surplus process modified by the payment of dividends when the insurer's surplus exceeds a threshold. We use a probabilistic argument to obtain general expressions for the expected present value of dividend payments, and show how these expressions can be applied for certain individual claim amount distributions. We then consider the question of maximising the expected present value of dividend payments subject to a constraint on the insurer's ruin probability.
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ItemThe density of the time to ruin in the classical Poisson risk modelDICKSON, DCM ; WILLMOT, E ( 2005)We derive an expression for the density of the time to ruin in the classical risk model by inverting its Laplace transform. We then apply the result when the individual claim amount distribution is a mixed Erlang distribution, and show how finite time ruin probabilities can be calculated in this case.