Mathematics

Research

18 pages, 1116 KiB

Open AccessArticle

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 293

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

Δ

CoES, 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

(This article belongs to the Special Issue Modeling, Analysis and Optimization for Mathematical Finance, Economics and Risks)

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31 pages, 396 KiB

Open AccessArticle

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 521

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

(This article belongs to the Special Issue Modeling, Analysis and Optimization for Mathematical Finance, Economics and Risks)

39 pages, 5234 KiB

Open AccessArticle

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 714

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

(This article belongs to the Special Issue Modeling, Analysis and Optimization for Mathematical Finance, Economics and Risks)

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12 pages, 252 KiB

Open AccessArticle

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 506

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

(This article belongs to the Special Issue Modeling, Analysis and Optimization for Mathematical Finance, Economics and Risks)

20 pages, 522 KiB

Open AccessArticle

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 625

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

(This article belongs to the Special Issue Modeling, Analysis and Optimization for Mathematical Finance, Economics and Risks)

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23 pages, 352 KiB

Open AccessArticle

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 761

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

(This article belongs to the Special Issue Modeling, Analysis and Optimization for Mathematical Finance, Economics and Risks)

16 pages, 360 KiB

Open AccessArticle

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 985

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

(This article belongs to the Special Issue Modeling, Analysis and Optimization for Mathematical Finance, Economics and Risks)

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20 pages, 1089 KiB

Open AccessArticle

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 762

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

(This article belongs to the Special Issue Modeling, Analysis and Optimization for Mathematical Finance, Economics and Risks)

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18 pages, 331 KiB

Open AccessArticle

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 813

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

{B_{1} (t), t \geq 0}

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

{B_{1} (t), t \geq 0}

and

{B_{2} (t), t \geq 0}

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

(This article belongs to the Special Issue Modeling, Analysis and Optimization for Mathematical Finance, Economics and Risks)

12 pages, 295 KiB

Open AccessArticle

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 734

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

(This article belongs to the Special Issue Modeling, Analysis and Optimization for Mathematical Finance, Economics and Risks)

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30 pages, 526 KiB

Open AccessArticle

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 2218

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

(This article belongs to the Special Issue Modeling, Analysis and Optimization for Mathematical Finance, Economics and Risks)

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11 pages, 316 KiB

Open AccessArticle

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 839

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

(This article belongs to the Special Issue Modeling, Analysis and Optimization for Mathematical Finance, Economics and Risks)

17 pages, 371 KiB

Open AccessArticle

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 1220

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

(This article belongs to the Special Issue Modeling, Analysis and Optimization for Mathematical Finance, Economics and Risks)

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