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Association Journal of CSIAM
Supervised by Ministry of Education of PRC
Sponsored by Xi'an Jiaotong University
ISSN 1005-3085  CN 61-1269/O1

Table of Content

    15 February 2024, Volume 41 Issue 1 Previous Issue   
    Robust Optimal Reinsurance and Investment Strategy with Delay under Mean-variance Premium Principle
    HU Jingming, LIU Wei, YAN Fang, HU Yijun
    2024, 41 (1):  1-16.  doi: 10.3969/j.issn.1005-3085.2024.01.001
    Abstract ( 74 )   Save
    The problem of robust optimal reinsurance and investment strategies for insurance companies with time delay are investigated. By purchasing proportional reinsurance, insurance companies can transfer a portion of their claim risks and pay reinsurance premiums based on the general mean-variance premium principle. At the same time, insurance companies invest their assets in a financial market consisting of a risk-free asset and a risky asset. Assume that the instantaneous expected return rate of the risky asset follows a mean-reverting Ornstein-Uhlenbeck (O-U) process. To maximize the exponential utility expectation of the insurance company's terminal wealth, dynamic programming principles are applied. By solving the Hamilton-Jacobi-Bellman (HJB) equation, the optimal reinsurance-investment strategy and the corresponding explicit expression of the value function are obtained. Furthermore, numerical analysis shows the impact of the main parameters on the optimal strategy. The results reveal that reinsurance strategy is mainly affected by the parameters of the insurance market and risk-free asset models, rather than the risky asset model or expected return rate. Time delay and robustness factors have a significant impact on the optimal reinsurance-investment strategy. Considering time delay improves the stability of the company's wealth while incorporating model uncertainty reduces the risk from inaccurate probability measures.
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    The Impact of Self-exciting Jump Process for the Short Term Model with Stochastic Volatility
    ZHANG Xinjun, JIANG Liang, LIN Qi, SONG Liping
    2024, 41 (1):  17-38.  doi: 10.3969/j.issn.1005-3085.2024.01.002
    Abstract ( 44 )   Save
    The stochastic volatility and self--exciting jump process are incorporated into a short-rate model. In the model, the self-exciting jump process will modeled by a Hawkes process, which captures the jump cluster. The expansion of the differential operator is applied to compute the closed-form moment function, and further develop the general moment method to estimate the parameters in the model and make statistical inference. The empirical results provide that there is no enough evidence to support the goodness of fit test. But the model with Hawkes process is significance in statistics, and  could strongly capture the jump clustering. Finally, the filtered values are estimated for the stochastic volatility, jump size, jump probability and intensity of jump by using filtering method. It is worth mention that the filtered jump probability is a plausible indicator to measure financial market stress.
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    A Multi-stage Portfolio Model Based on Genetic Differential Co-evolution in an Fuzzy Environment
    HU Chenyang, GAO Yuelin, SUN Ying
    2024, 41 (1):  39-52.  doi: 10.3969/j.issn.1005-3085.2024.01.003
    Abstract ( 48 )   Save
    Investment in real economic activities is generally uncertain and stochastic, and investors' choice of risky assets is of multi-stage in most cases. Based on this reality, multiple frictions in a fuzzy environment are considered and a base constraint is proposed on assets using transaction restrictions to develop a likelihood mean-lower half-variance-entropy multi-stage portfolio optimization model (V-S-M), which is a multi-stage mixed integer programming problem. A genetic differential co-evolutionary algorithm (GAHDE) for solving the model is presented to analyse the portfolio strategy under different risk attitudes, and the numerical results are compared with the likelihood mean-lower half variance model (V-M) and the likelihood mean-entropy model (S-M), as well as with standard genetic algorithms (GA) and differential evolution algorithms (DE). The results validated the superiority and effectiveness of the model and algorithm designed in this paper.
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    Research on Hierarchical Cooperating Distribution of Emergency Materials for Public Emergency
    LIU Huwei, ZHOU Li, YANG Jianglong
    2024, 41 (1):  53-66.  doi: 10.3969/j.issn.1005-3085.2024.01.004
    Abstract ( 35 )   Save
    In order to achieve material classification and cooperating distribution under the unified supply management system of emergency materials in the event of a public emergency, the importance of emergency materials was divided into several levels according to the specific emergency situation. In accordance with the principle of priority distribution of important materials, a model for the hierarchical and cooperating distribution of materials between multiple warehouses was been established, which could integrate and optimize transportation vehicles and various emergency materials throughout the region. The model took the shortest total distribution time as the optimization objective, combined cooperating distribution with time series decision-making, considered the delivery process of all vehicles between warehouses and demand points as the time series decision-making process of multi-agent collaboration, reduced the computational complexity of multi-agent and multi-task assignment problem, and made the algorithm of time series decision-making model still applicable in the case of large-scale problems. In addition, on the basis of improving the variable input and output dimensions of LSTM (Long Short Term Mermory) network, combined with the theoretical framework of genetic algorithm (GA), the LSTM-GA algorithm for this problem was designed, and a study simulation was carried out. It was found that the convergence speed and stability of LSTM-GA algorithm were improved compared with single algorithm. The results show that the LSTM-GA algorithm can realize the variable dimensions of LSTM network receiving and output information, and is an effective method to study the hierarchical and cooperating distribution of emergency materials.
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    Research on Bond Default Early Warning Model of Listed Companies in China Based on Feature Selection and Default Identification
    BAI Yuming, JIANG Yuxi
    2024, 41 (1):  67-87.  doi: 10.3969/j.issn.1005-3085.2024.01.005
    Abstract ( 71 )   Save
    In order to select the indicators of bond default, to determine an effective default warning time window, and to establish a bond default warning model which is practically and has high prediction accuracy in different default states, SMOTE and XGBoost are applied to process imbalanced samples and determine the default warning model and the optimal warning time window according to the default warning accuracy and the number of indicators in the indicator system respectively. The results show that the prediction effect is better when the default warning time window is $t-1$, which means that using indicator data one year in advance can better predict whether bonds will default. Using the embedding feature selection of XGBoost algorithm to establish the default early warning model can complete the model training and indicator system dimension reduction simultaneously, which makes the compute easier. Comparing with the other 7 common default prediction methods, the proposed model has higher default prediction accuracy, more effective dimension reduction, less computing time, and stronger interpretability.
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    Sampling Theorem for Stochastic Process and Random Field from Local Average
    ZHANG Shuo
    2024, 41 (1):  88-110.  doi: 10.3969/j.issn.1005-3085.2024.01.006
    Abstract ( 51 )   Save
    The research of random signal sampling has become one of the mainstream directions in sampling theory in the past few decades, it has been widely concerned in the field of information and mathematics in both theory and practical application. In recent years, a series of research results on local average sampling of random processes and random fields have been obtained in the sampling theory. Firstly, the defects and limitations of sampling theorem in its application are analyzed. Secondly, the development and related results for the local average sampling theorem of stochastic process, multidimensional stochastic process,random field and spatio-temporal random field are introduced systematically. Finally, the further research directions of the spatiotemporal random field sampling problem are pointed out. The results show that the local average sampling method improves the sampling accuracy and approximation effect, and the random field local average sampling theory has important applications in wave parameter inversion and marine pollution monitoring. In particular, the research of the spatiotemporal random field sampling theory based on mixed norm not only has important theoretical value, but also has application value in engineering field.
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    A Cyclic Algorithm for Low Rank Tensor Completion
    WANG Junxia, GUO Xiongwei, WANG Chuanlong
    2024, 41 (1):  111-126.  doi: 10.3969/j.issn.1005-3085.2024.01.007
    Abstract ( 67 )   Save
    To solve the tensor completion problem, a cyclic algorithm for low rank tensor completion is proposed. Based on the alternating direction multiplier method, the sub-problem is circularly updated, which effectively reduces the cost of tensor expansion, matrix folding and singular value decomposition in the iterative process. At the same time, the convergence analysis of the algorithm is given under reasonable assumptions. Finally, the numerical experiments show that the proposed algorithm is more efficient than other algorithm.
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    Weight Distribution of Augmented Codes Based on Quadratic Gauss Sums
    HENG Ziling, CHEN Fuling, LI Dexiang, LIU Fenjin
    2024, 41 (1):  127-144.  doi: 10.3969/j.issn.1005-3085.2024.01.008
    Abstract ( 45 )   Save
    Cyclic codes are an important subclass of linear codes as they have efficient encoding and decoding algorithms and they are widely used in many areas including communication and data storage. The weight distribution is an interesting research subject of cyclic codes. How to construct cyclic codes with only a few weights is an important research problem in the coding theory. To solve this problem, the augmented codes of a class of cyclic codes are investigated based on quadratic Gauss sums and some basic properties of characters over finite fields. The weight distribution and parameters of the augmented code are presented. It turns out that the augmented codes are projective cyclic codes with only a few weights. Compared with the original cyclic code, the augmented codes have higher transmission efficiency. The duals of the augmented codes are optimal or nearly optimal according to the sphere-packing bound. As a byproduct, the complete weight distribution of the original cyclic codes is also given.
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    Dynamical Analysis of Stochastic SIRS Double Epidemic Model with Logistic Growth and Crowley-Martin Incidence Rate
    ZHAO Yanjun, SU Li, SUN Xiaohui, LI Wenxuan
    2024, 41 (1):  145-163.  doi: 10.3969/j.issn.1005-3085.2024.01.009
    Abstract ( 65 )   Save
    Based on the fact that many diseases coexist in real life and are affected by environmental noise, a stochastic SIRS double epidemic model with Logistic growth and Crowley-Martin type incidence is established to discuss the effects of Logistic growth, Crowley-Martin type incidence and double epidemic infectious diseases on the global dynamics of the model. It is obtained that the global dynamics of the model is determined by stochastic basic reproduction number. Firstly, by constructing the Lyapunov function and using the Ito's formula, the existence and uniqueness of the global positive solution are proved, and then, by combining the stochastic basic reproduction number and the constructed Lyapunov function, the sufficient conditions for determining the extinction and persistence of the disease are obtained by using the LaSalle invariance principle. The results show that the environmental change can inhibit the disease under certain conditions. Finally, the correctness of the theoretical results is verified by numerical simulation.
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    Multi-scale Transformer for View-based 3D Shape Analysis
    WEI Xin, SUN Jian
    2024, 41 (1):  164-174.  doi: 10.3969/j.issn.1005-3085.2024.01.010
    Abstract ( 152 )   Save
    View-based 3D shape analysis is a crucial research domain within the field of 3D computer vision. Those techniques aim to recognise and retrieve 3D objects by aggregating features extracted from 2D images of the same object taken from different viewpoints. However, effectively exploring the relationships between different viewpoints and aggregating features from multiple viewpoints using these relationships remain fundamental challenges in the field of 3D shape analysis. Taking inspiration from the recent success of Transformer networks in modeling relationships, an novel multi-scale Transformer architecture is introduced and the Multi-View Multi-Scale Transformer (MVMST) is presented for three-dimensional shape analysis. MVMST efficiently learns relationships between different views and integrates features from multi-view images into a global descriptor. While previous approaches use a Transformer with a global receptive field to model the relationships between multi-view features, MVMST makes use of multi-scale learning. A multi-scale Transformer is used to model the relationships between multi-view features at different scales. In addition, a multi-scale fusion module is designed to merge the features processed by the multi-scale Transformer to obtain a more efficient multi-scale representation. With the view pooling module, these multi-scale representations from different views are eventually fused into a global descriptor of the 3D shape. The experiments on synthetic and real-world 3D object classification datasets demonstrate that the proposed method shows promising performance in 3D object classification tasks.
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    The Anti-plane Fracture Problem of Four Edge Cracks Emanating from a Square Hole in Magnetoelectroelastic Materials
    XU Yan, YANG Juan
    2024, 41 (1):  175-185.  doi: 10.3969/j.issn.1005-3085.2024.01.011
    Abstract ( 10 )   Save
    The fracture problem of the magnetic electro-elastic material with four cracks in a square hole is investigated under the action of anti-plane shear force. Based on the linear elastic fracture theory and the Riemann-Schwarz analytical continuation theorem, by constructing a suitable numerical conformal mapping function and the residue theorem, the boundary value problem of the analytical function is transformed into Cauchy integral equations, then the explicit expression of fracture mechanics parameters at the crack tip under magnetoelectric impermeable boundary conditions is obtained. The effectiveness of the method is verified by comparing with the existing results. The effects of hole size, four crack lengths and mechano-electro-magnetic load on crack propagation parameters are described by numerical examples. The results show that the effect of the horizontal right crack on the crack growth is more significant. Vertical crack affects the propagation trend of horizontal crack. Under magnetoelectric impermeable boundary conditions, the stress intensity factor of crack tip increases with the increase of mechanical load. However, the propagation of crack under electric and magnetic load is closely related to the magnitude and direction of mechanical load. The analytical method developed provides an effective way to solve the problem of intelligent composite materials in complex multi-connected domains, and the research results provide a scientific basis for the optimal design of composite materials or structures with cracks.
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    VOFFLC Control of Wave Equation Based on FFT
    WANG Yang, JIANG Houshun, WANG Jie, XU Dongjin, YIN Biao
    2024, 41 (1):  186-198.  doi: 10.3969/j.issn.1005-3085.2024.01.012
    Abstract ( 33 )   Save
    The infinite-dimensional properties of complex wave equations is transformed from time-domain PDE model to frequency-domain ODE model using FFT method based on Simulink platform, and then a control system is created which is comparable to the centralized parameter in the frequency domain. It is demonstrated that the idea of using the FFT principle to simulate the wave equation of a PDE is correct by comparing the experimental results of FFT and mature FDM simulation; adaptive VOFFLC closed-loop control is applied to the frequency domain ODE model, and two control feedback rules are designed. When VOFFLC control with a multiplication rule is applied to one of them, the wave has the same form as the original one, but the period is shortened and the amplitude is lowered. When VOFFLC control with the subtraction rule is used, it can achieve results similar to boundary control; however, vector-level control in the spatial dimension can be achieved, i.e., vector-level control of any function shape, interpolation function, or scatter point in that dimension, which boundary control cannot do. As a result, the FFT-based VOFFLC control of wave equations has significant research implications as well as extensive practical utility.
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