Economics - Research Publications

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Author: Dickson, David × Subject: Finance and Investment ×

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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).
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    Optimal Dividends Under a Ruin Probability Constraint
    Dickson, 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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    Some Optimal Dividends Problems
    Dickson, DCM ; Waters, HR (Cambridge University Press (CUP), 2004-05)
    We consider a situation originally discussed by De Finetti (1957) in which a surplus process is modified by the introduction of a constant dividend barrier. We extend some known results relating to the distribution of the present value of dividend payments until ruin in the classical risk model and show how a discrete time risk model can be used to provide approximations when analytic results are unavailable. We extend the analysis by allowing the process to continue after ruin.
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    The density of the time to ruin in the classical Poisson risk model
    DICKSON, 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.