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Selected Papers from the 6th Gerber-Shiu Workshop and the 3rd...
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Selected Papers from the 6th Gerber-Shiu Workshop and the 3rd Modeling of Heavy-Tail Phenomena Workshop

A special issue of Risks (ISSN 2227-9091).

Deadline for manuscript submissions: closed (28 February 2017) | Viewed by 32310

Special Issue Editor

Prof. Dr. Qihe Tang

E-Mail Website
Guest Editor
Department of Statistics and Actuarial Science, University of Iowa, 241 Schaeffer Hall, Iowa City, IA 52242-1409, USA
Interests: extreme value theory for insurance and finance; quantitative risk management; multivariate heavy-tailed distributions
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The journal Risks has launched a Special Issue for papers from The Sixth International Gerber-Shiu Workshop and The Third International Workshop on Statistical Modeling of Heavy-Tail Phenomena with Applications.

The International Gerber-Shiu Workshop has been held biennially since 2006 and has become an important platform for exchanging research ideas and disseminating recent advances in risk theory and related fields. The Sixth International Gerber-Shiu Workshop, hosted by Renmin University of China, will be held on June 8–9, 2016, and is open to academic researchers and industry practitioners from all over the world. Topics of the workshop range from recent theoretical and methodological developments in risk theory and related fields to novel applications in insurance, finance, and risk management. Keynote speakers are Hansjörg Albrecher (University of Lausanne), Søren Asmussen (Aarhus University), Sergey Foss (Heriot-Watt University), Jose Garrido (Concordia University), Dmitry Korshunov (Lancaster University), Elias S. W. Shiu (University of Iowa), and Hailiang Yang (University of Hong Kong).

Heavy-tail phenomena exist everywhere and often express themselves in the form of natural or man-made catastrophes. They have attracted much attention from academics and practitioners in finance, insurance, information science, and environmental science. The Third International Workshop on Statistical Modeling of Heavy-Tail Phenomena with Applications, hosted by Zhejiang Gongshang University will be held on June 4–5, 2016, and will be attended by a gathering of researchers in related fields from all over the world. Keynote speakers are Hansjörg Albrecher (University of Lausanne), Søren Asmussen (Aarhus University), Sergey Foss (Heriot-Watt University), Dmitry Korshunov (Lancaster University), Qihe Tang (University of Iowa), and Yuebao Wang (Soochow University).

We invite all participants to submit their manuscripts presented at these two workshops to this Special Issue for peer-review and processing prior to publication in the online journal, Risks.

Prof. Qihe Tang
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Risks is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

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Published Papers (7 papers)

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Research

258 KiB  
Article
Ruin Probabilities in a Dependent Discrete-Time Risk Model With Gamma-Like Tailed Insurance Risks
by Xing-Fang Huang, Ting Zhang, Yang Yang and Tao Jiang
Risks 2017, 5(1), 14; https://doi.org/10.3390/risks5010014 - 3 Mar 2017
Cited by 9 | Viewed by 4164
Abstract
This paper considered a dependent discrete-time risk model, in which the insurance risks are represented by a sequence of independent and identically distributed real-valued random variables with a common Gamma-like tailed distribution; the financial risks are denoted by another sequence of independent and [...] Read more.
This paper considered a dependent discrete-time risk model, in which the insurance risks are represented by a sequence of independent and identically distributed real-valued random variables with a common Gamma-like tailed distribution; the financial risks are denoted by another sequence of independent and identically distributed positive random variables with a finite upper endpoint, but a general dependence structure exists between each pair of the insurance risks and the financial risks. Following the works of Yang and Yuen in 2016, we derive some asymptotic relations for the finite-time and infinite-time ruin probabilities. As a complement, we demonstrate our obtained result through a Crude Monte Carlo (CMC) simulation with asymptotics. Full article
(This article belongs to the Special Issue Selected Papers from the 6th Gerber-Shiu Workshop and the 3rd Modeling of Heavy-Tail Phenomena Workshop)
995 KiB  
Article
Distinguishing Log-Concavity from Heavy Tails
by Søren Asmussen and Jaakko Lehtomaa
Risks 2017, 5(1), 10; https://doi.org/10.3390/risks5010010 - 7 Feb 2017
Cited by 8 | Viewed by 4575
Abstract
Well-behaved densities are typically log-convex with heavy tails and log-concave with light ones. We discuss a benchmark for distinguishing between the two cases, based on the observation that large values of a sum X 1 + X 2 occur as result of a [...] Read more.
Well-behaved densities are typically log-convex with heavy tails and log-concave with light ones. We discuss a benchmark for distinguishing between the two cases, based on the observation that large values of a sum X 1 + X 2 occur as result of a single big jump with heavy tails whereas X 1 , X 2 are of equal order of magnitude in the light-tailed case. The method is based on the ratio | X 1 − X 2 | / ( X 1 + X 2 ) , for which sharp asymptotic results are presented as well as a visual tool for distinguishing between the two cases. The study supplements modern non-parametric density estimation methods where log-concavity plays a main role, as well as heavy-tailed diagnostics such as the mean excess plot. Full article
(This article belongs to the Special Issue Selected Papers from the 6th Gerber-Shiu Workshop and the 3rd Modeling of Heavy-Tail Phenomena Workshop)
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1070 KiB  
Article
Optimal Reinsurance Policies under the VaR Risk Measure When the Interests of Both the Cedent and the Reinsurer Are Taken into Account
by Wenjun Jiang, Jiandong Ren and Ričardas Zitikis
Risks 2017, 5(1), 11; https://doi.org/10.3390/risks5010011 - 5 Feb 2017
Cited by 14 | Viewed by 6197
Abstract
Optimal forms of reinsurance policies have been studied for a long time in the actuarial literature. Most existing results are from the insurer’s point of view, aiming at maximizing the expected utility or minimizing the risk of the insurer. However, as pointed out [...] Read more.
Optimal forms of reinsurance policies have been studied for a long time in the actuarial literature. Most existing results are from the insurer’s point of view, aiming at maximizing the expected utility or minimizing the risk of the insurer. However, as pointed out by Borch (1969), it is understandable that a reinsurance arrangement that might be very attractive to one party (e.g., the insurer) can be quite unacceptable to the other party (e.g., the reinsurer). In this paper, we follow this point of view and study forms of Pareto-optimal reinsurance policies whereby one party’s risk, measured by its value-at-risk (VaR), cannot be reduced without increasing the VaR of the counter-party in the reinsurance transaction. We show that the Pareto-optimal policies can be determined by minimizing linear combinations of the VaR s of the two parties in the reinsurance transaction. Consequently, we succeed in deriving user-friendly, closed-form, optimal reinsurance policies and their parameter values. Full article
(This article belongs to the Special Issue Selected Papers from the 6th Gerber-Shiu Workshop and the 3rd Modeling of Heavy-Tail Phenomena Workshop)
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372 KiB  
Article
n-Dimensional Laplace Transforms of Occupation Times for Spectrally Negative Lévy Processes
by Xuebing Kuang and Xiaowen Zhou
Risks 2017, 5(1), 8; https://doi.org/10.3390/risks5010008 - 29 Jan 2017
Cited by 2 | Viewed by 3810
Abstract
Using a Poisson approach, we find Laplace transforms of joint occupation times over n disjoint intervals for spectrally negative Lévy processes. They generalize previous results for dimension two. Full article
(This article belongs to the Special Issue Selected Papers from the 6th Gerber-Shiu Workshop and the 3rd Modeling of Heavy-Tail Phenomena Workshop)
363 KiB  
Article
Optimal Reinsurance Under General Law-Invariant Convex Risk Measure and TVaR Premium Principle
by Mi Chen, Wenyuan Wang and Ruixing Ming
Risks 2016, 4(4), 50; https://doi.org/10.3390/risks4040050 - 16 Dec 2016
Cited by 2 | Viewed by 3802
Abstract
In this paper, we study the optimal reinsurance problem where risks of the insurer are measured by general law-invariant risk measures and premiums are calculated under the TVaR premium principle, which extends the work of the expected premium principle. Our objective is to [...] Read more.
In this paper, we study the optimal reinsurance problem where risks of the insurer are measured by general law-invariant risk measures and premiums are calculated under the TVaR premium principle, which extends the work of the expected premium principle. Our objective is to characterize the optimal reinsurance strategy which minimizes the insurer’s risk measure of its total loss. Our calculations show that the optimal reinsurance strategy is of the multi-layer form, i.e., f * ( x ) = x ∧ c * + ( x - d * ) + with c * and d * being constants such that 0 ≤ c * ≤ d * . Full article
(This article belongs to the Special Issue Selected Papers from the 6th Gerber-Shiu Workshop and the 3rd Modeling of Heavy-Tail Phenomena Workshop)
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921 KiB  
Article
How Does Reinsurance Create Value to an Insurer? A Cost-Benefit Analysis Incorporating Default Risk
by Ambrose Lo
Risks 2016, 4(4), 48; https://doi.org/10.3390/risks4040048 - 16 Dec 2016
Cited by 4 | Viewed by 5446
Abstract
Reinsurance is often empirically hailed as a value-adding risk management strategy which an insurer can utilize to achieve various business objectives. In the context of a distortion-risk-measure-based three-party model incorporating a policyholder, insurer and reinsurer, this article formulates explicitly the optimal insurance–reinsurance strategies [...] Read more.
Reinsurance is often empirically hailed as a value-adding risk management strategy which an insurer can utilize to achieve various business objectives. In the context of a distortion-risk-measure-based three-party model incorporating a policyholder, insurer and reinsurer, this article formulates explicitly the optimal insurance–reinsurance strategies from the perspective of the insurer. Our analytic solutions are complemented by intuitive but scientifically rigorous explanations on the marginal cost and benefit considerations underlying the optimal insurance–reinsurance decisions. These cost-benefit discussions not only cast light on the economic motivations for an insurer to engage in insurance with the policyholder and in reinsurance with the reinsurer, but also mathematically formalize the value created by reinsurance with respect to stabilizing the loss portfolio and enlarging the underwriting capacity of an insurer. Our model also allows for the reinsurer’s failure to deliver on its promised indemnity when the regulatory capital of the reinsurer is depleted by the reinsured loss. The reduction in the benefits of reinsurance to the insurer as a result of the reinsurer’s default is quantified, and its influence on the optimal insurance–reinsurance policies analyzed. Full article
(This article belongs to the Special Issue Selected Papers from the 6th Gerber-Shiu Workshop and the 3rd Modeling of Heavy-Tail Phenomena Workshop)
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369 KiB  
Article
A Note on Upper Tail Behavior of Liouville Copulas
by Lei Hua
Risks 2016, 4(4), 40; https://doi.org/10.3390/risks4040040 - 8 Nov 2016
Cited by 3 | Viewed by 3667
Abstract
The family of Liouville copulas is defined as the survival copulas of multivariate Liouville distributions, and it covers the Archimedean copulas constructed by Williamson’s d-transform. Liouville copulas provide a very wide range of dependence ranging from positive to negative dependence in the [...] Read more.
The family of Liouville copulas is defined as the survival copulas of multivariate Liouville distributions, and it covers the Archimedean copulas constructed by Williamson’s d-transform. Liouville copulas provide a very wide range of dependence ranging from positive to negative dependence in the upper tails, and they can be useful in modeling tail risks. In this article, we study the upper tail behavior of Liouville copulas through their upper tail orders. Tail orders of a more general scale mixture model that covers Liouville distributions is first derived, and then tail order functions and tail order density functions of Liouville copulas are derived. Concrete examples are given after the main results. Full article
(This article belongs to the Special Issue Selected Papers from the 6th Gerber-Shiu Workshop and the 3rd Modeling of Heavy-Tail Phenomena Workshop)
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