On the expected discounted penalty function at ruin of a surplus process with interest

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    Author
    Cai, Jun; Dickson, David C.M.
    Date
    2001-11
    University of Melbourne Author/s
    Cai, Jun; Dickson, David
    Affiliation
    Economics and Commerce: Centre for Actuarial Studies
    Metadata
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    Document Type
    Preprint
    Citations
    Cai, Jun and Dickson, David C.M. (2001) On the expected discounted penalty function at ruin of a surplus process with interest.
    Access Status
    Open Access
    URI
    http://hdl.handle.net/11343/33692
    Description

    ISBN 073402135621348 research paper no. 91.
    Abstract
    In this paper, we study the expected value of a discounted penalty function at ruin of the classical surplus process modified by the inclusion of interest of the surplus. The 'penalty' is simply a function of the surplus immediately prior to ruin and the deficit at ruin. An integral equation for the expected value is derived, while the exact solution is given when the initial surplus is zero. Dickson's (1992) formulae for the distribution of the surplus immediately prior to ruin in the classical surplus process are generalised to our modified surplus process.
    Keywords
    ruin penalty function; surplus prior to ruin; deficit at ruin; Laplace transform; Volterra equation; compound Poisson process; force of interest; risk theory; renewal process; random walk.

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