On the expected discounted penalty function at ruin of a surplus process with interest
AuthorCai, Jun; Dickson, David C.M.
AffiliationEconomics and Commerce: Centre for Actuarial Studies
CitationsCai, Jun and Dickson, David C.M. (2001) On the expected discounted penalty function at ruin of a surplus process with interest.
Access StatusOpen Access
ISBN 073402135621348 research paper no. 91.
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.
Keywordsruin 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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