A link between wave governed random motions and ruin processes

By Christian Mazza, Didier Rullière. 2004

61 citations recorded by the source corpus.

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.

Subfields: Demography, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/e848ce59ef7aef104b319b4688061981bafae076

Citations in the corpus

• On a Periodic Dividend Barrier Strategy in the Dual Model with Continuous Monitoring of Solvency (2013, unknown): “Because of its duality to the classical Cramér-Lundberg model, the model described in (1.1) was first referred to as the ‘dual risk model’ by Mazza and Rullière (2004).”