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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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ItemThe density of the time to ruin for a Sparre Andersen process with Erlang arrivals and exponential claimsDickson, David C. M. ; Hughes, Barry D. ; Lianzeng, Zhang ( 2003-10)We derive expressions for the density of the time to ruin given that ruin occurs in a Sparre Andersen model in which individual claim amounts are exponentially distributed and inter-arrival times are distributed as Erlang(n, β). We provide numerical illustrations of finite time ruin probabilities, as well as illustrating features of the density functions.
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ItemDe Vylder Approximations to the Moments and Distribution of the Time to RuinDickson, David C M ; Wong, Kwok Swan ( 2004-02)De Vylder (1978) proposed a method of approximating the probability of ultimate ruin in the classical risk model. In this paper we show that his ideas can be extended to approximate the moments and distribution of the time to ruin
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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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ItemThe joint distribution of the surplus prior to ruin and the deficit at ruin in some Sparre Andersen modelsDICKSON, DCM ; DREKIC, S ( 2004)
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ItemThe Distribution of the time to Ruin in the Classical Risk ModelDickson, DCM ; Waters, HR (Cambridge University Press (CUP), 2002-01-01)Abstract We study the distribution of the time to ruin in the classical risk model. We consider some methods of calculating this distribution, in particular by using algorithms to calculate finite time ruin probabilities. We also discuss calculation of the moments of this distribution.
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ItemThe Gerber-Shiu discounted penalty function in the stationary renewal risk modelWillmot, Gordon E. ; Dickson, David C. M. ( 2002-08)The discounted penalty function introduced by Gerber and Shiu (1998) is considered in the stationary renewal risk model, where it is expressed in terms of the same discounted penalty function in the ordinary renewal risk model. This relationship unifies and generalizes known special cases. An invariance property between the stationary renewal risk model and the classical Poisson model with respect to the ruin probability is also generalized as a result.
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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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ItemUpper bounds for ultimate ruin probabilities in the Sparre Andersen model with interestCAI, J ; DICKSON, DCM ( 2003)
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