Martingales and the distribution of the time to ruin

Martin Jacobsen

Stochastic Processes and their Applications, 2003, vol. 107, issue 1, 29-51

Abstract: We determine the ultimate ruin probability and the Laplace transform of the distribution of the time to ruin in the classical risk model, where claims arrive according to a renewal process, with waiting times that are of phase-type, while the claims themselves follow a distribution with a Laplace transform that is a rational function. The main tools are martingales, the optional sampling theorem and results from the theory of piecewise deterministic Markov processes.

Keywords: Risk; process; Probability; of; ruin; Time; to; ruin; Martingales; Optional; sampling; Piecewise; deterministic; Markov; processes (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (4)

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