Modeling, Analysis and Optimization for Mathematical Finance, Economics and Risks

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

Deadline for manuscript submissions: 31 May 2024 | Viewed by 11804

Special Issue Editors


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Guest Editor
1. Center for Financial Engineering, Soochow University, Suzhou 215006, China
2. Actuarial Research Center, University of Haifa, Haifa 31905, Israel
Interests: risk measure; portfolio theory; risk modelling; fintech and insurtech

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Guest Editor
School of Finance, Zhongnan University of Economics and Law, Wuhan 430073, China
Interests: risk management; dependence modelling; time series analysis

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Guest Editor
College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, China
Interests: actuarial science; risk management; decentralize insurance

Special Issue Information

Dear Colleagues,

Financial and economic markets are currently characterized by an increasing number of challenging tasks, inflationary environments, energy prices, contractions from the labor markets and credit risk, etc. To respond to the ever-changing market, business, and financial and economic environment, academicians and practitioners constantly endeavor to develop advanced theories, methods, models, and algorithms to solve the needs arising in risk measure and management and investment.

In this Special Issue, we aim to contribute to the enrichment of modeling, analysis and optimization for risks in finance, insurance, and economics. We seek considerable contributions to the development and implementation of advanced mathematical and instrumental methods, analysis, and applications in the fields of but not limited to financial and economic risk modeling and management.

Prof. Dr. Jing Yao
Dr. Xiang Hu
Dr. Jingchao Li
Guest Editors

Manuscript Submission Information

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Keywords

  • risk measurement and management
  • optimal investment
  • risk modelling and analysis time series analysis
  • insurance
  • fintech and insurtech

Published Papers (13 papers)

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Research

18 pages, 1116 KiB  
Article
Measurement and Forecasting of Systemic Risk: A Vine Copula Grouped-CoES Approach
by Huiting Duan, Jinghu Yu and Linxiao Wei
Mathematics 2024, 12(8), 1233; https://doi.org/10.3390/math12081233 - 19 Apr 2024
Viewed by 189
Abstract
Measuring systemic risk plays an important role in financial risk management to control systemic risk. By means of a vine copula grouped-CoES method, this paper aims to measure the systemic risk of Chinese financial markets. The empirical study indicates that the banking industry [...] Read more.
Measuring systemic risk plays an important role in financial risk management to control systemic risk. By means of a vine copula grouped-CoES method, this paper aims to measure the systemic risk of Chinese financial markets. The empirical study indicates that the banking industry has a low risk and a strong ability to resist risks, but also contributes the most of the systemic risk. On the other hand, insurance companies and securities have high ES but low ΔCoES, indicating their low risk tolerance and small contribution to the systemic risk. Furthermore, this study employs a sliding window in Monte Carlo simulation to forecast systemic risk. The findings of this paper suggest that different types of financial industries should adopt different systemic risk measures. Full article
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31 pages, 396 KiB  
Article
Robust Portfolio Choice under the Modified Constant Elasticity of Variance
by Wei Li Fan and Marcos Escobar Anel
Mathematics 2024, 12(3), 440; https://doi.org/10.3390/math12030440 - 30 Jan 2024
Viewed by 497
Abstract
This study investigates ambiguity aversion within the framework of a utility-maximizing investor under a modified constant-elasticity-of-volatility (M-CEV) model for the underlying asset. We derive closed-form solutions of a non-affine type for the optimal allocation and value function via a Cauchy problem. This work [...] Read more.
This study investigates ambiguity aversion within the framework of a utility-maximizing investor under a modified constant-elasticity-of-volatility (M-CEV) model for the underlying asset. We derive closed-form solutions of a non-affine type for the optimal allocation and value function via a Cauchy problem. This work generalizes previous results in non-ambiguous settings by extending existing work to Hyperbolic Absolute Risk Aversion utility (HARA), correcting some typos in the literature for Constant Relative Risk Aversion utility (CRRA). Helpful details and derivations are also included in the manuscript. Full article
39 pages, 5234 KiB  
Article
Identifying Hidden Factors Associated with Household Emergency Fund Holdings: A Machine Learning Application
by Wookjae Heo, Eunchan Kim, Eun Jin Kwak and John E. Grable
Mathematics 2024, 12(2), 182; https://doi.org/10.3390/math12020182 - 05 Jan 2024
Viewed by 674
Abstract
This paper describes the results from a study designed to illustrate the use of machine learning analytical techniques from a household consumer perspective. The outcome of interest in this study is a household’s degree of financial preparedness as indicated by the presence of [...] Read more.
This paper describes the results from a study designed to illustrate the use of machine learning analytical techniques from a household consumer perspective. The outcome of interest in this study is a household’s degree of financial preparedness as indicated by the presence of an emergency fund. In this study, six machine learning algorithms were evaluated and then compared to predictions made using a conventional regression technique. The selected ML algorithms showed better prediction performance. Among the six ML algorithms, Gradient Boosting, kNN, and SVM were found to provide the most robust degree of prediction and classification. This paper contributes to the methodological literature in consumer studies as it relates to household financial behavior by showing that when prediction is the main purpose of a study, machine learning techniques provide detailed yet nuanced insights into behavior beyond traditional analytic methods. Full article
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12 pages, 252 KiB  
Article
Optimal Debt Ratio and Dividend Payment Policies for Insurers with Ambiguity
by Dan Zhu, Cuixia Chen and Bing Liu
Mathematics 2024, 12(1), 40; https://doi.org/10.3390/math12010040 - 22 Dec 2023
Viewed by 479
Abstract
This study considers the optimal debt ratio and dividend payment policies for an insurer concerned about model misspecification. We assume that the insurer can invest all of its asset to the financial market and the ambiguity may exist in the risky asset. Taking [...] Read more.
This study considers the optimal debt ratio and dividend payment policies for an insurer concerned about model misspecification. We assume that the insurer can invest all of its asset to the financial market and the ambiguity may exist in the risky asset. Taking into account the ambiguous situation, the insurer aims to maximize the expected utility of a discounted dividend payment until it ruins. Under some assumption, we prove that there exists classical solutions of the optimal debt ratio, dividend payment policies, and value functions that show that the existence of ambiguity can affect the optimal debt ratio and dividend policies significantly. Full article
20 pages, 522 KiB  
Article
Robust and Sparse Portfolio: Optimization Models and Algorithms
by Hongxin Zhao, Yilun Jiang and Yizhou Yang
Mathematics 2023, 11(24), 4925; https://doi.org/10.3390/math11244925 - 11 Dec 2023
Cited by 1 | Viewed by 593
Abstract
The robust and sparse portfolio selection problem is one of the most-popular and -frequently studied problems in the optimization and financial literature. By considering the uncertainty of the parameters, the goal is to construct a sparse portfolio with low volatility and decent returns, [...] Read more.
The robust and sparse portfolio selection problem is one of the most-popular and -frequently studied problems in the optimization and financial literature. By considering the uncertainty of the parameters, the goal is to construct a sparse portfolio with low volatility and decent returns, subject to other investment constraints. In this paper, we propose a new portfolio selection model, which considers the perturbation in the asset return matrix and the parameter uncertainty in the expected asset return. We define three types of stationary points of the penalty problem: the Karush–Kuhn–Tucker point, the strong Karush–Kuhn–Tucker point, and the partial minimizer. We analyze the relationship between these stationary points and the local/global minimizer of the penalty model under mild conditions. We design a penalty alternating-direction method to obtain the solutions. Compared with several existing portfolio models on seven real-world datasets, extensive numerical experiments demonstrate the robustness and effectiveness of our model in generating lower volatility. Full article
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23 pages, 352 KiB  
Article
From Transience to Recurrence for Cox–Ingersoll–Ross Model When b < 0
by Mingli Zhang and Gaofeng Zong
Mathematics 2023, 11(21), 4485; https://doi.org/10.3390/math11214485 - 30 Oct 2023
Viewed by 746
Abstract
We consider the Cox–Ingersoll–Ross (CIR) model in time-dependent domains, that is, the CIR process in time-dependent domains reflected at the time-dependent boundary. This is a very meaningful question, as the CIR model is commonly used to describe interest rate models, and interest rates [...] Read more.
We consider the Cox–Ingersoll–Ross (CIR) model in time-dependent domains, that is, the CIR process in time-dependent domains reflected at the time-dependent boundary. This is a very meaningful question, as the CIR model is commonly used to describe interest rate models, and interest rates are often artificially set within a time-dependent domain by policy makers. We consider the most fundamental question of recurrence versus transience for normally reflected CIR process with time-dependent domains, and we examine some precise conditions for recurrence versus transience in terms of the growth rates of the boundary. The drift terms and the diffusion terms of the CIR processes in time-dependent domains are carefully provided. In the transience case, we also investigate the last passage time, while in the case of recurrence, we also consider the positive recurrence of the CIR processes in time-dependent domains. Full article
16 pages, 360 KiB  
Article
Tariff Analysis in Automobile Insurance: Is It Time to Switch from Generalized Linear Models to Generalized Additive Models?
by Zuleyka Díaz Martínez, José Fernández Menéndez and Luis Javier García Villalba
Mathematics 2023, 11(18), 3906; https://doi.org/10.3390/math11183906 - 14 Sep 2023
Viewed by 923
Abstract
Generalized Linear Models (GLMs) are the standard tool used for pricing in the field of automobile insurance. Generalized Additive Models (GAMs) are more complex and computationally intensive but allow taking into account nonlinear effects without the need to discretize the explanatory variables. In [...] Read more.
Generalized Linear Models (GLMs) are the standard tool used for pricing in the field of automobile insurance. Generalized Additive Models (GAMs) are more complex and computationally intensive but allow taking into account nonlinear effects without the need to discretize the explanatory variables. In addition, they fit perfectly into the mental framework shared by actuaries and are easier to use and interpret than machine learning models, such as trees or neural networks. This work compares both the GLM and GAM approaches, using a wide sample of policies to assess their differences in terms of quality of predictions, complexity of use, and time of execution. The results show that GAMs are a powerful alternative to GLMs, particularly when “big data” implementations of GAMs are used. Full article
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20 pages, 1089 KiB  
Article
Optimal Defined Contribution Pension Management with Jump Diffusions and Common Shock Dependence
by Wujun Lv, Linlin Tian and Xiaoyi Zhang
Mathematics 2023, 11(13), 2954; https://doi.org/10.3390/math11132954 - 02 Jul 2023
Viewed by 740
Abstract
This work deals with an optimal asset allocation problem for a defined contribution (DC) pension plan during its accumulation phase. The contribution rate is assumed to be proportional to the individual’s salary. The salary follows a Heston stochastic volatility model with jumps, and [...] Read more.
This work deals with an optimal asset allocation problem for a defined contribution (DC) pension plan during its accumulation phase. The contribution rate is assumed to be proportional to the individual’s salary. The salary follows a Heston stochastic volatility model with jumps, and there exists common shock dependence between the salary and the volatility. Since the time horizon of pension management is quite long, the influence of inflation is considered in the given context. The aim of the pension plan described in this paper is to reduce fluctuations in terminal wealth by investing in the bond and the stock. Through the dynamic programming principle, the Hamilton–Jacobi–Bellman equation is shown. The explicit expression of the investment decision is derived by solving the Hamilton–Jacobi–Bellman equation. In the last part, a numerical analysis is shown to illustrate the impacts of different parameters on the optimal investment policy. Full article
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18 pages, 331 KiB  
Article
Finite-Time Ruin Probabilities of Bidimensional Risk Models with Correlated Brownian Motions
by Dan Zhu, Ming Zhou and Chuancun Yin
Mathematics 2023, 11(12), 2767; https://doi.org/10.3390/math11122767 - 19 Jun 2023
Viewed by 797
Abstract
The present work concerns the finite-time ruin probabilities for several bidimensional risk models with constant interest force and correlated Brownian motions. Under the condition that the two Brownian motions {B1(t),t0} and [...] Read more.
The present work concerns the finite-time ruin probabilities for several bidimensional risk models with constant interest force and correlated Brownian motions. Under the condition that the two Brownian motions {B1(t),t0} and {B2(t),t0} are correlated, we establish new results for the finite-time ruin probabilities. Our research enriches the development of the ruin theory with heavy tails in unidimensional risk models and the dependence theory of stochastic processes. Full article
12 pages, 295 KiB  
Article
Perturbed Skew Diffusion Processes
by Yingxu Tian and Haoyan Zhang
Mathematics 2023, 11(11), 2417; https://doi.org/10.3390/math11112417 - 23 May 2023
Viewed by 712
Abstract
This work investigates whether there uniquely exists a solution to the perturbed skew diffusion process. We construct the solution by iteration and divide the whole time interval into parts on which we disperse the perturbed skew diffusion process into two tractable portions, one [...] Read more.
This work investigates whether there uniquely exists a solution to the perturbed skew diffusion process. We construct the solution by iteration and divide the whole time interval into parts on which we disperse the perturbed skew diffusion process into two tractable portions, one for perturbed diffusion process, the other for skew diffusion process. After this disposition, we only focus on the process in each time interval. Noticing the continuity on every time interval boundaries generalized by a sequence of stopping times, we acquire the main result of this paper as well as a time change for the perturbed skew process. Full article
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30 pages, 526 KiB  
Article
Estimating the Gerber–Shiu Function in the Two-Sided Jumps Risk Model by Laguerre Series Expansion
by Kang Hu, Ya Huang and Yingchun Deng
Mathematics 2023, 11(9), 1994; https://doi.org/10.3390/math11091994 - 23 Apr 2023
Viewed by 2193
Abstract
In this paper, we consider an insurance risk model with two-sided jumps, where downward and upward jumps typically represent claim amounts and random gains, respectively. We use the Laguerre series to expand the Gerber–Shiu function and estimate it based on observed information. Moreover, [...] Read more.
In this paper, we consider an insurance risk model with two-sided jumps, where downward and upward jumps typically represent claim amounts and random gains, respectively. We use the Laguerre series to expand the Gerber–Shiu function and estimate it based on observed information. Moreover, we show that the estimator is easily computed and has a fast convergence rate. Numerical examples are also provided to show the efficiency of our method when the sample size is finite. Full article
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11 pages, 316 KiB  
Article
Two Generalizations of the Core Inverse in Rings with Some Applications
by San-Zhang Xu, Julio Benítez, Ya-Qian Wang and Dijana Mosić
Mathematics 2023, 11(8), 1822; https://doi.org/10.3390/math11081822 - 12 Apr 2023
Viewed by 816
Abstract
In this paper, we introduce two new generalized core inverses, namely, the (p,q,m)-core inverse and the p,q,n-core inverse; both extend the inverses of the i,m [...] Read more.
In this paper, we introduce two new generalized core inverses, namely, the (p,q,m)-core inverse and the p,q,n-core inverse; both extend the inverses of the i,m-core inverse, the (j,m)-core inverse, the core inverse, the core-EP inverse and the DMP-inverse. Full article
17 pages, 371 KiB  
Article
Robust Optimal Investment Strategies with Exchange Rate Risk and Default Risk
by Wei Wang, Qianyan Li, Quan Li and Song Xu
Mathematics 2023, 11(6), 1550; https://doi.org/10.3390/math11061550 - 22 Mar 2023
Cited by 1 | Viewed by 1183
Abstract
The problem of robust optimal investment with exchange rate risk and default risk is studied. We assume that investors are ambiguity averse and they have access not only to the domestic market but also to the foreign market. The corresponding Hamilton–Jacobi–Bellman (HJB) equations [...] Read more.
The problem of robust optimal investment with exchange rate risk and default risk is studied. We assume that investors are ambiguity averse and they have access not only to the domestic market but also to the foreign market. The corresponding Hamilton–Jacobi–Bellman (HJB) equations are first obtained through the robust stochastic optimal control theory. Then, we discuss the optimal investment problems before and after default, and the value functions and optimal investment strategies are obtained. Finally, we find that the optimal investment strategies of pre-default are affected by the intensity of default and the credit spread, and the investors cannot hold defaultable bonds in the post-default case. Numerical results also show that the exchange rate risk, default risk and ambiguity aversion have a great effect on the optimal investment strategies. Full article
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