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23 pages, 746 KiB

Open AccessArticle

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 893

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

(This article belongs to the Special Issue Advances in Mathematical Modelling and Statistical Methods for Risk Management)

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14 pages, 280 KiB

Open AccessArticle

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 4 | Viewed by 1788

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

(This article belongs to the Special Issue Advances in Mathematical Modelling and Statistical Methods for Risk Management)

19 pages, 1788 KiB

Open AccessArticle

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 985

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

(This article belongs to the Special Issue Advances in Mathematical Modelling and Statistical Methods for Risk Management)

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37 pages, 948 KiB

Open AccessArticle

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 - 4 Jul 2023

Cited by 7 | Viewed by 1105

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

(This article belongs to the Special Issue Advances in Mathematical Modelling and Statistical Methods for Risk Management)

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11 pages, 280 KiB

Open AccessArticle

Monotone Mean L^p-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 984

Abstract

In this paper, we establish a new coherent risk measure on

L^{p}

, which we refer to as the monotone mean

L^{p}

-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

L^{p}

, which we refer to as the monotone mean

L^{p}

-deviation risk measure. Then, the related properties are discussed. Furthermore, from the perspective of acceptance set, we discuss the relationship between the monotone mean

L^{p}

-deviation risk measure and the monotone Sharpe ratio risk measure. Finally, we extend the monotone mean

L^{p}

-deviation risk measure to the multivariate setting. Full article

(This article belongs to the Special Issue Advances in Mathematical Modelling and Statistical Methods for Risk Management)

25 pages, 596 KiB

Open AccessArticle

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 - 7 Feb 2023

Viewed by 1570

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

(This article belongs to the Special Issue Advances in Mathematical Modelling and Statistical Methods for Risk Management)

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16 pages, 1964 KiB

Open AccessArticle

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 2487

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

(This article belongs to the Special Issue Advances in Mathematical Modelling and Statistical Methods for Risk Management)

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19 pages, 465 KiB

Open AccessArticle

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 - 2 Oct 2022

Viewed by 1347

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

(This article belongs to the Special Issue Advances in Mathematical Modelling and Statistical Methods for Risk Management)

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