On the moments of dividends and capital injections under a variant type of Parisian ruin

IF 0.9 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters Pub Date : 2024-08-23 DOI:10.1016/j.spl.2024.110225

Kaixin Yan , Ruixing Ming , Haibin Wang , Wenyuan Wang

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引用次数: 0

Abstract

This paper considers a risk model driven by a spectrally negative Lévy process, where any surplus above $b$ ( $0 < b < \infty$ ) is deducted away as dividends and any deficit is covered by injected capitals/raised money. For such a risk model, we define a variant of Parisian ruin time as the first time that the surplus process stays continuously below $a$ ( $0 < a < b < \infty$ ) for a time interval with length larger than some pre-specified exponential random variable that is marked on this time interval. A recursive formula for the moments of the Net Present Value (NPV) of dividends paid until Parisian ruin is provided. The expected NPV of capitals injected until the Parisian ruin time is also characterized compactly in terms of the scale functions of the underlying process.

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论巴黎废墟变异类型下的股息和注资时刻

本文考虑了一个由光谱负莱维过程驱动的风险模型，其中任何高于 b（0<b<∞）的盈余都会作为股息被扣除，而任何赤字都会由注入的资本/筹集的资金来弥补。对于这种风险模型，我们将巴黎毁灭时间的变种定义为：盈余过程第一次持续低于 a（0<a<b<∞）的时间间隔，该时间间隔的长度大于某个预先指定的指数随机变量，该指数随机变量在该时间间隔上有标记。提供了巴黎毁灭前股息净现值（NPV）矩的递推公式。根据基本过程的尺度函数，还可以紧凑地描述在巴黎毁灭时间之前注入资本的预期净现值。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Statistics & Probability Letters 数学-统计学与概率论

CiteScore

1.60

自引率

0.00%

发文量

173

审稿时长

6 months

期刊介绍： Statistics & Probability Letters adopts a novel and highly innovative approach to the publication of research findings in statistics and probability. It features concise articles, rapid publication and broad coverage of the statistics and probability literature. Statistics & Probability Letters is a refereed journal. Articles will be limited to six journal pages (13 double-space typed pages) including references and figures. Apart from the six-page limitation, originality, quality and clarity will be the criteria for choosing the material to be published in Statistics & Probability Letters. Every attempt will be made to provide the first review of a submitted manuscript within three months of submission. The proliferation of literature and long publication delays have made it difficult for researchers and practitioners to keep up with new developments outside of, or even within, their specialization. The aim of Statistics & Probability Letters is to help to alleviate this problem. Concise communications (letters) allow readers to quickly and easily digest large amounts of material and to stay up-to-date with developments in all areas of statistics and probability. The mainstream of Letters will focus on new statistical methods, theoretical results, and innovative applications of statistics and probability to other scientific disciplines. Key results and central ideas must be presented in a clear and concise manner. These results may be part of a larger study that the author will submit at a later time as a full length paper to SPL or to another journal. Theory and methodology may be published with proofs omitted, or only sketched, but only if sufficient support material is provided so that the findings can be verified. Empirical and computational results that are of significant value will be published.