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2 results

Some Finite Time Ruin Problems
D. C. M. Dickson
Journal:

Annals of Actuarial Science / Volume 2 / Issue 2 / September 2007

Published online by Cambridge University Press:

10 May 2011, pp. 217-232
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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).

The joint density of the maximum and its location for a Wiener process with drift
L. A. Shepp
Journal:

Journal of Applied Probability / Volume 16 / Issue 2 / June 1979

Published online by Cambridge University Press:

14 July 2016, pp. 423-427

Print publication:

June 1979
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We give a simple expression for the joint probability density of: (a) the maximum value Y = max [X(t), 0 ≦ t ≦ T); (b) its location ; (c) the endpoint X(T), where X(t) = Xc(t) is a Wiener process with drift, Xc(t) = W(t) + ct, 0 ≦ t ≦ T. That is, we find the density p(θ, y, x) = p(θ, y, x; c, T) of , Y, X(T), p(θ, y, x; , Xc(T) ∈ dx) is given by, 0 < θ < T, x ≦ y, 0 < y,