A link between wave governed random motions and ruin processes

Christian Mazza () and Didier Rulliere ()
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Christian Mazza: Département de Mathématiques - Albert-Ludwigs-Universität Freiburg = University of Freiburg

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Abstract: This article establishes a link between hitting times associated with the risk process (time of ruin) and wave governed random motions, which are widely used in physics. Concerning risk theory, another link holds between processes corresponding to models called positive and negative risk sums. Some classical results appear to be strongly interconnected. An original algorithm is proposed for computing finite-time ruin probabilities in renewal non-Poissonian risk model with exponential claims. Concerning wave-governed random motions, we analyze the distribution of the maxima of the processes. New bounds are directly derived from risk theory and appear to be more accurate than the ones proposed recently in the probabilistic literature. Finally, we propose applications of these notions in finance.

Keywords: Renewal models; Wave-governed random motions; Persistent random motions; Telegraph equation; Negative risk sums; Non-poissonian ruin model (search for similar items in EconPapers)
Date: 2004-12-07
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Citations: View citations in EconPapers (15)

Published in Insurance: Mathematics and Economics, 2004, 35 (2), pp.205-222. ⟨10.1016/j.insmatheco.2004.07.014⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00412977

DOI: 10.1016/j.insmatheco.2004.07.014

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