Economics - Research Publications

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Start date: 2003 × End date: 2010 × Author: Dickson, David ×

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    The density of the time to ruin for a Sparre Andersen process with Erlang arrivals and exponential claims
    Dickson, 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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    De Vylder Approximations to the Moments and Distribution of the Time to Ruin
    Dickson, 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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    Optimal Dividends under a Ruin ProbabilityConstraint
    Dickson, 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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    Optimal dynamic reinsurance
    Dickson, 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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    On the distribution of the deficit at ruin when claims are phase-type
    Drekic, S ; DICKSON, D ; Stanford, DA ; Willmot, GE ( 2005)
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    Optimal dynamic reinsurance
    DICKSON, D. ; WATERS, H. ( 2006)
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    Some Finite Time Ruin Problems
    Dickson, 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).