Recursive methods for a multi-dimensional risk process with common shocks

Lan Gong, Andrei L. Badescu and Eric C.K. Cheung

Insurance: Mathematics and Economics, 2012, vol. 50, issue 1, 109-120

Abstract: In this paper, a multi-dimensional risk model with common shocks is studied. Using a simple probabilistic approach via observing the risk processes at claim instants, recursive integral formulas are developed for the survival probabilities as well as for a class of Gerber–Shiu expected discounted penalty functions that include the surplus levels at ruin. Under the assumption of exponential or mixed Erlang claims, the recursive integrals can be simplified to give recursive sums which are computationally more tractable. Numerical examples including an optimal capital allocation problem are also given towards the end.

Keywords: Common shock; Deficit at ruin; Gerber–Shiu expected discounted penalty function; Recursive methods; Survival probability; Multi-dimensional risk process; Optimal capital allocation (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (15)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:50:y:2012:i:1:p:109-120

DOI: 10.1016/j.insmatheco.2011.10.007

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