Economics - Research Publications

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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.
On the distribution of the deficit at ruin when claims are phase-type

Drekic, S ; DICKSON, D ; Stanford, DA ; Willmot, GE ( 2005)
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.