Surplus analysis for a class of Coxian interclaim time distributions with applications to mixed Erlang claim amounts

DOI10.1016/J.INSMATHECO.2009.08.004zbMath1231.91250OpenAlexW1970102885MaRDI QIDQ659179

Gordon E. Willmot, Jae-Kyung Woo

Publication date: 10 February 2012

Published in: Insurance Mathematics \& Economics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.insmatheco.2009.08.004

zbMATH Keywords

Lagrange polynomialsdefective renewal equationladder heightSparre Andersen risk process\(K_{n}\) family of distributionscombination of Erlangscompound geometric distributiongeneralized Lundberg's fundamental equationmixtures of Erlangs

Mathematics Subject Classification ID

Applications of statistics to actuarial sciences and financial mathematics (62P05) Renewal theory (60K05)

Related Items (8)

On the time value of Parisian ruin in (dual) renewal risk processes with exponential jumps ⋮ The Gerber-Shiu discounted penalty function: a review from practical perspectives ⋮ On the analysis of a general class of dependent risk processes ⋮ Some Remarks on Delayed Renewal Risk Models ⋮ A generalized penalty function in Sparre Andersen risk models with surplus-dependent premium ⋮ On the moments of the time to ruin in dependent Sparre Andersen models with emphasis on Coxian interclaim times ⋮ On orderings and bounds in a generalized Sparre Andersen risk model ⋮ A generalized penalty function for a class of discrete renewal processes

Cites Work

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• Structural properties of Gerber-Shiu functions in dependent Sparre Andersen models
• On ruin for the Erlang \((n)\) risk process
• On the discounted penalty function in the renewal risk model with general interclaim times
• The surpluses immediately before and at ruin, and the amount of the claim causing ruin
• On the Class of Erlang Mixtures with Risk Theoretic Applications
• On the Joint Distributions of the Time to Ruin, the Surplus Prior to Ruin, and the Deficit at Ruin in the Classical Risk Model
• On a general class of renewal risk process: analysis of the Gerber-Shiu function
• The Time Value of Ruin in a Sparre Andersen Model
• On the Time Value of Ruin
• Moment generating functions of compound renewal sums with discounted claims
• Loss Models

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