On a Generalization from Ruin to Default in a Lévy Insurance Risk Model

Runhuan Feng () and Yasutaka Shimizu ()
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Runhuan Feng: University of Wisconsin—Milwaukee
Yasutaka Shimizu: Osaka University

Methodology and Computing in Applied Probability, 2013, vol. 15, issue 4, 773-802

Abstract: Abstract In a variety of insurance risk models, ruin-related quantities in the class of expected discounted penalty function (EDPF) were known to satisfy defective renewal equations that lead to explicit solutions. Recent development in the ruin literature has shown that similar defective renewal equations exist for a more general class of quantities than that of EDPF. This paper further extends the analysis of this new class of functions in the context of a spectrally negative Lévy risk model. In particular, we present an operator-based approach as an alternative analytical tool in comparison with fluctuation theoretic methods used for similar quantities in the current literature. The paper also identifies a sufficient and necessary condition under which the classical results from defective renewal equation and those from fluctuation theory are interchangeable. As a by-product, we present a series representation of scale function as well as potential measure in terms of compound geometric distribution.

Keywords: Expected discounted penalty function; Costs up to default; Defective renewal equation; Compound geometric distribution; Lévy risk model; Scale function; Potential measure; Operator calculus; 91B30; 60J45; 60G51 (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11009-012-9282-y

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