Advances in Mathematical Modelling and Statistical Methods for Risk Management

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Financial Mathematics".

Deadline for manuscript submissions: 30 April 2024 | Viewed by 8348

Special Issue Editors


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Guest Editor
College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Interests: probabilistic modelling in reliability and safety; risk propagation in complex networks; machine learning

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Guest Editor
Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei 230026, China
Interests: risk measures; risk management; extreme value theory; decision theory; stochastic dominance
Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada
Interests: quantitative risk management; extreme value theory; actuarial science

Special Issue Information

Dear Colleagues,

We would like to invite you to submit your recent research to the Special Issue titled “Advances in Mathematical Modelling and Statistical Methods for Risk Management”, appearing in the journal Mathematics. This issue will provide an opportunity for researchers to present up-to-date mathematical and statistical methods for modeling risks, such as market, credit, operational risks, in the field of risk management. The broad applications can be found in, but are not restricted to, finance, economics, actuarial science, and reliability. We welcome high-quality research papers that address areas including, but not limited to, risk measures, extreme value theory, reliability, actuarial science, and mathematical finance in general.  

Prof. Dr. Gaofeng Da
Dr. Tiantian Mao
Dr. Fan Yang
Guest Editors

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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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.

Keywords

  • risk measures
  • risk management
  • extreme value analysis
  • distributionally robust optimization
  • dependence measures
  • copulas
  • portfolio
  • risk propagation
  • systemic risk
  • reliability assessment
  • stochastic ordering
  • complex networks
  • mathematical finance

Published Papers (8 papers)

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Research

23 pages, 746 KiB  
Article
Distributionally Robust Reinsurance with Glue Value-at-Risk and Expected Value Premium
by Wenhua Lv and Linxiao Wei
Mathematics 2023, 11(18), 3923; https://doi.org/10.3390/math11183923 - 15 Sep 2023
Viewed by 575
Abstract
In this paper, we explore a distributionally robust reinsurance problem that incorporates the concepts of Glue Value-at-Risk and the expected value premium principle. The problem focuses on stop-loss reinsurance contracts with known mean and variance of the loss. The optimization problem can be [...] Read more.
In this paper, we explore a distributionally robust reinsurance problem that incorporates the concepts of Glue Value-at-Risk and the expected value premium principle. The problem focuses on stop-loss reinsurance contracts with known mean and variance of the loss. The optimization problem can be formulated as a minimax problem, where the inner problem involves maximizing over all distributions with the same mean and variance. It is demonstrated that the inner problem can be represented as maximizing either over three-point distributions under some mild condition or over four-point distributions otherwise. Additionally, analytical solutions are provided for determining the optimal deductible and optimal values. Full article
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14 pages, 280 KiB  
Article
Media Tone and Stock Price Crash Risk: Evidence from China
by Ruwei Zhao, Ruixin Fan, Xiong Xiong, Jianli Wang and Jitka Hilliard
Mathematics 2023, 11(17), 3675; https://doi.org/10.3390/math11173675 - 25 Aug 2023
Cited by 1 | Viewed by 890
Abstract
Following the 2008 financial crisis, multiple studies have contributed to the research on stock price crashes. However, most of the studies on stock price crashes are from the corporate management perspective, focusing on factors such as the board’s character, the CEO’s power, the [...] Read more.
Following the 2008 financial crisis, multiple studies have contributed to the research on stock price crashes. However, most of the studies on stock price crashes are from the corporate management perspective, focusing on factors such as the board’s character, the CEO’s power, the brand’s capital, and ESG performance. Few studies have taken external information, such as media coverage, into consideration. Meanwhile, in the era of 5G, internet media has witnessed exponential growth, heavily enhancing the speed of information transmission; this could possibly impact the future risk associated with stock price crashes. From this perspective, our study extends the coverage by investigating the relationship between internet media coverage and the potential risk of stock price crashes. Using a comprehensive dataset of the Chinese stock market from 2008 to 2021, we found that the optimistic (pessimistic) tones of internet media were positively (negatively) correlated with the future risk of crashes. These findings remained firm after accounting for winsorization, corporate governance control, firm fixed effects, and instrumental variable analysis. Further analyses showed that media tone impacts were more pronounced for firms with higher analyst coverage. Our study indicates that investors, especially retail investors, who are more easily influenced by internet media, should be more cautious about the increasingly favorable internet coverage of listed companies, which could result in a heightened future risk of stock price crashes. Moreover, regulators should inform investors when listed companies are experiencing more favorable internet coverage to minimize potential stock market fluctuations and investment losses for investors. Full article
19 pages, 1788 KiB  
Article
Research on Financial Default Model with Stochastic Intensity Using Filtered Likelihood Method
by Xiangdong Liu, Jiahui Wu and Xianglong Li
Mathematics 2023, 11(14), 3061; https://doi.org/10.3390/math11143061 - 11 Jul 2023
Viewed by 677
Abstract
This paper investigates the financial default model with stochastic intensity by incomplete data. On the strength of the process-designated point process, the likelihood function of the model in the parameter estimation can be decomposed into the factor likelihood term and event likelihood term. [...] Read more.
This paper investigates the financial default model with stochastic intensity by incomplete data. On the strength of the process-designated point process, the likelihood function of the model in the parameter estimation can be decomposed into the factor likelihood term and event likelihood term. The event likelihood term can be successfully estimated by the filtered likelihood method, and the factor likelihood term can be calculated in a standardized manner. The empirical study reveals that, under the filtered likelihood method, the first model outperforms the other in terms of parameter estimation efficiency, convergence speed, and estimation accuracy, and has a better prediction effect on the default data in China’s financial market, which can also be extended to other countries, which is of great significance in the default risk control of financial institutions. Full article
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37 pages, 948 KiB  
Article
Exploring New Horizons: Advancing Data Analysis in Kidney Patient Infection Rates and UEFA Champions League Scores Using Bivariate Kavya–Manoharan Transformation Family of Distributions
by Aisha Fayomi, Ehab M. Almetwally and Maha E. Qura
Mathematics 2023, 11(13), 2986; https://doi.org/10.3390/math11132986 - 04 Jul 2023
Cited by 4 | Viewed by 746
Abstract
In survival analyses, infections at the catheter insertion site among kidney patients using portable dialysis machines pose a significant concern. Understanding the bivariate infection recurrence process is crucial for healthcare professionals to make informed decisions regarding infection management protocols. This knowledge enables the [...] Read more.
In survival analyses, infections at the catheter insertion site among kidney patients using portable dialysis machines pose a significant concern. Understanding the bivariate infection recurrence process is crucial for healthcare professionals to make informed decisions regarding infection management protocols. This knowledge enables the optimization of treatment strategies, reduction in complications associated with infection recurrence and improvement of patient outcomes. By analyzing the bivariate infection recurrence process in kidney patients undergoing portable dialysis, it becomes possible to predict the probability, timing, risk factors and treatment outcomes of infection recurrences. This information aids in identifying the likelihood of future infections, recognizing high-risk patients in need of close monitoring, and guiding the selection of appropriate treatment approaches. Limited bivariate distribution functions pose challenges in jointly modeling inter-correlated time between recurrences with different univariate marginal distributions. To address this, a Copula-based methodology is presented in this study. The methodology introduces the Kavya–Manoharan transformation family as the lifetime model for experimental units. The new bivariate models accurately measure dependence, demonstrate significant properties, and include special sub-models that leverage exponential, Weibull, and Pareto distributions as baseline distributions. Point and interval estimation techniques, such as maximum likelihood and Bayesian methods, where Bayesian estimation outperforms maximum likelihood estimation, are employed, and bootstrap confidence intervals are calculated. Numerical analysis is performed using the Markov chain Monte Carlo method. The proposed methodology’s applicability is demonstrated through the analysis of two real-world data-sets. The first data-set, focusing on infection and recurrence time in kidney patients, indicates that the Farlie–Gumbel–Morgenstern bivariate Kavya–Manoharan–Weibull (FGMBKM-W) distribution is the best bivariate model to fit the kidney infection data-set. The second data-set, specifically that related to UEFA Champions League Scores, reveals that the Clayton Kavya–Manoharan–Weibull (CBKM-W) distribution is the most suitable bivariate model for fitting the UEFA Champions League Scores. This analysis involves examining the time elapsed since the first goal kicks and the home team’s initial goal. Full article
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11 pages, 280 KiB  
Article
Monotone Mean Lp-Deviation Risk Measures
by Jinyang Zhang, Linxiao Wei and Yijun Hu
Mathematics 2023, 11(12), 2706; https://doi.org/10.3390/math11122706 - 15 Jun 2023
Viewed by 663
Abstract
In this paper, we establish a new coherent risk measure on Lp, which we refer to as the monotone mean Lp-deviation risk measure. Then, the related properties are discussed. Furthermore, from the perspective of acceptance set, we discuss the [...] Read more.
In this paper, we establish a new coherent risk measure on Lp, which we refer to as the monotone mean Lp-deviation risk measure. Then, the related properties are discussed. Furthermore, from the perspective of acceptance set, we discuss the relationship between the monotone mean Lp-deviation risk measure and the monotone Sharpe ratio risk measure. Finally, we extend the monotone mean Lp-deviation risk measure to the multivariate setting. Full article
25 pages, 596 KiB  
Article
Shortfall-Based Wasserstein Distributionally Robust Optimization
by Ruoxuan Li, Wenhua Lv and Tiantian Mao
Mathematics 2023, 11(4), 849; https://doi.org/10.3390/math11040849 - 07 Feb 2023
Viewed by 1049
Abstract
In this paper, we study a distributionally robust optimization (DRO) problem with affine decision rules. In particular, we construct an ambiguity set based on a new family of Wasserstein metrics, shortfall–Wasserstein metrics, which apply normalized utility-based shortfall risk measures to summarize the transportation [...] Read more.
In this paper, we study a distributionally robust optimization (DRO) problem with affine decision rules. In particular, we construct an ambiguity set based on a new family of Wasserstein metrics, shortfall–Wasserstein metrics, which apply normalized utility-based shortfall risk measures to summarize the transportation cost random variables. In this paper, we demonstrate that the multi-dimensional shortfall–Wasserstein ball can be affinely projected onto a one-dimensional one. A noteworthy result of this reformulation is that our program benefits from finite sample guarantee without a dependence on the dimension of the nominal distribution. This distributionally robust optimization problem also has computational tractability, and we provide a dual formulation and verify the strong duality that enables a direct and concise reformulation of this problem. Our results offer a new DRO framework that can be applied in numerous contexts such as regression and portfolio optimization. Full article
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16 pages, 1964 KiB  
Article
Tail Value-at-Risk-Based Expectiles for Extreme Risks and Their Application in Distributionally Robust Portfolio Selections
by Haoyu Chen and Kun Fan
Mathematics 2023, 11(1), 91; https://doi.org/10.3390/math11010091 - 26 Dec 2022
Cited by 1 | Viewed by 1724
Abstract
Empirical evidence suggests that financial risk has a heavy-tailed profile. Motivated by recent advances in the generalized quantile risk measure, we propose the tail value-at-risk (TVaR)-based expectile, which can capture the tail risk compared with the classic expectile. In addition to showing that [...] Read more.
Empirical evidence suggests that financial risk has a heavy-tailed profile. Motivated by recent advances in the generalized quantile risk measure, we propose the tail value-at-risk (TVaR)-based expectile, which can capture the tail risk compared with the classic expectile. In addition to showing that the risk measure is well-defined, the properties of TVaR-based expectiles as risk measures were also studied. In particular, we give the equivalent characterization of the coherency. For extreme risks, usually modeled by a regularly varying survival function, the asymptotic expansion of a TVaR-based expectile (with respect to quantiles) was studied. In addition, motivated by recent advances in distributionally robust optimization in portfolio selections, we give the closed-form of the worst-case TVaR-based expectile based on moment information. Based on this closed form of the worst-case TVaR-based expectile, the distributionally robust portfolio selection problem is reduced to a convex quadratic program. Numerical results are also presented to illustrate the performance of the new risk measure compared with classic risk measures, such as tail value-at-risk-based expectiles. Full article
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19 pages, 465 KiB  
Article
Some Results on Measures of Interaction among Risks
by Yiting Fan and Rui Fang
Mathematics 2022, 10(19), 3611; https://doi.org/10.3390/math10193611 - 02 Oct 2022
Viewed by 1042
Abstract
It has become a common understanding that financial risk can spread rapidly from one institution to another, and the stressful status of one institution may finally result in a systemic crisis. One popular method to assess and quantify the risk of contagion is [...] Read more.
It has become a common understanding that financial risk can spread rapidly from one institution to another, and the stressful status of one institution may finally result in a systemic crisis. One popular method to assess and quantify the risk of contagion is employing the co-risk measures and risk contribution measures. It is interesting and important to understand how the underlining dependence structure and magnitude of random risks jointly affect systemic risk measures. In this paper, we mainly focus on the conditional value-at-risk, conditional expected shortfall, the delta conditional value-at-risk, and the delta conditional expected shortfall. Existing studies mainly focus on the situation with two random risks, and this paper makes some contributions by considering the scenario with possibly more than two random risks. By employing the tools of stochastic order, positive dependence concepts and arrangement monotonicity, several results concerning the usual stochastic order, increasing convex order, dispersive order and excess wealth order are presented. Concisely speaking, it is found that for a large enough stress level, a larger random risk tends to lead to a more severe systemic risk. We also performed some Monte Carlo experiments as illustrations for the theoretical findings. Full article
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