Economics - Research Publications

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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)
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.
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.