On a generalization of the expected discounted penalty function to include deficits at and beyond ruin

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• 作者：Zied Ben Salah (1)
  
• 关键词：Ruin ; Spectrally negative Lévy process ; Scale function ; Gerber–Shiu function ; Laplace transform ; Capital injections.
• 刊名：European Actuarial Journal
• 出版年：2014
• 出版时间：July 2014
• 年：2014
• 卷：4
• 期：1
• 页码：219-246
• 全文大小：
• 参考文献：1. Asmussen S, Albrecher H (2010) Ruin probabilities. World Scientific Publishing, London
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  14. Huzak M, Perman M, Sikic H, Vondracek Z (2004) Ruin probabilities and decompositions for general perturbed risk processes. Ann Appl Probab 14(3):1378-397 CrossRef
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• 作者单位：Zied Ben Salah (1)
  
  1. Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Blvd West, Montreal, Quebec, H3G 1M8, Canada
  
• ISSN：2190-9741

文摘

In this paper we propose an extended concept of the expected discounted penalty function (EDPF) that takes into account new ruin-related random variables. In the well-known EDPF introduced in seminal papers by Gerber and Shiu?(Insur Math Econ 21:129-37, 1997, N Am Actuar J 2(1):48-8, 1998) and Gerber and Landry?(Insur Math Econ 22:263-76, 1998), we consider the expectation of a sequence of discounted penalty functions of new record minima reached by a claim of the risk process after ruin (and before recovery). Inspired by results of Huzak et al. (Ann Appl Probab 14(3):1378-397, 2004) and developments in fluctuation theory for spectrally negative Lévy processes, we provide a characterization for this extended EDPF in a setting involving a cumulative claims modeled by a subordinator, and Brownian perturbation. We illustrate how the extended EDPF can be used to compute the expected discounted value of capital injections for the Brownian perturbed risk model.