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15 June 2018, Volume 35 Issue 3 Previous Issue    Next Issue

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Optimal Reinsurance and Investment Strategies under CIR Stochastic Interest Rate Model ZHOU Rui, RONG Xi-min, ZHAO Hui 2018, 35 (3):  245-257.  doi: 10.3969/j.issn.1005-3085.2018.03.001 Abstract ( 256 )   PDF (579KB) ( 449 )   Save This paper considers an optimal reinsurance and optimal investment problem under the Cox-Ingersoll-Roll (CIR) stochastic interest rate framework. We assume that the insurer can invest in cash,zero coupon bond and several kinds of stocks in the financial market. Meanwhile, proportion reinsurance is purchased by an insurer to transfer the risk of insurance to other insurance companies. We further adopt an affine CIR model to characterize the interest rate while the surplus wealth process is approximated by a diffusion process, namely, the jump process is approximated by a continuous process. The goal of the insurer is to maximize the expected power utility of the terminal wealth. Due to the fact that the surplus process of the insurer is not a self-financing process, we firstly transform the original problem into a self-financing problem, establish the corresponding Hamilton-Jacobi-Bellman equation, and then derive an explicit solution via the stochastic optimal control method. We find that the percentage of quota invested in stocks would decrease with the increase of risk aversion parameters, while the terminal wealth would increase with the increase of initial interest rate. Finally, sensitivity analysis is carried out to show the impact of financial parameters on the optimal strategies and optimal utility. Related Articles | Metrics

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Risk Measures Based on Probability Semimetric WEN Ping, QIN Ling-li 2018, 35 (3):  258-268.  doi: 10.3969/j.issn.1005-3085.2018.03.002 Abstract ( 159 )   PDF (172KB) ( 361 )   Save In the financial risk management, research on the method of risk measures has always been an important topic. We use probability metric and convex function to construct a new risk measure. Since the risk measure does not satisfy tonicity and the idea of downside risk, we use convex function to construct new risk measures based on the probability semi-metric. It is found that the new risk measurement method includes many common risk measures, for example, semi-variance, semi-absolute deviation, the lower partial moment and ES. We show that the risk measure not only satisfies the convexity but also satisfies tonicity. Considering the importance of convexity and tonicity in portfolio selection and risk management, the proposed risk measure has certain theoretical value and practical significance. Related Articles | Metrics

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Robust Adaptive Output-feedback Control of Cascade Systems with Unknown Control Directions AN Hai-long, LIU Tao 2018, 35 (3):  269-282.  doi: 10.3969/j.issn.1005-3085.2018.03.003 Abstract ( 168 )   PDF (278KB) ( 270 )   Save This paper studies the robust adaptive output-feedback control problem for a class of nonlinear cascade systems with unknown control directions. The original system with unknown directions is firstly transformed into a new system without unknown control direction by using the linear transformation. Then, based on the linear high gains observer and Nussbaum function, a novel robust adaptive output-feedback controller is proposed. Furthermore, it is proved that all the closed-loop signals remain bounded and the states asymptotically converge to the origin under the controller. Furthermore, a sufficient condition for the asymptotic stability of the closed-loop system is derived by constructing a new Lyapunov function. Finally, a simulation example is given to illustrate the effectiveness of the proposed control laws. Related Articles | Metrics

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Well-posedness of the Parallel System Sustained by a Cold Standby Unit and Attended by a Repairman with a Single Vacation ZHOU Xue-liang, LIU Fen-jin 2018, 35 (3):  283-394.  doi: 10.3969/j.issn.1005-3085.2018.03.004 Abstract ( 146 )   PDF (162KB) ( 223 )   Save We study the well-posedness of the Gaver's parallel system sustained by a cold standby unit and attended by a repairman with a single vacation by utilizing the linear operator semigroup theory. It is assumed that the operating times of the units satisfy exponential distributions, the repair times and the vacation time of the repairman satisfy general continuous distributions. By normalizing the system described by differential equations, we convert the system equations into an abstract Cauchy problem in the Banach space through introducing a state space, main operators and their domains. With the help of the Hille-Yosida theorem, Phillips theorem and Fattorini theorem in functional analysis, we prove that the parallel system has a unique and positive time-dependent solution which satisfies probability condition. Related Articles | Metrics

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The Generalized Entropy Ergodic Theorem for Homogeneous Markov Chains Indexed by a Homogeneous Tree YANG Jie, YANG Wei-guo 2018, 35 (3):  295-307.  doi: 10.3969/j.issn.1005-3085.2018.03.005 Abstract ( 181 )   PDF (163KB) ( 302 )   Save In this paper, we study the generalized entropy ergodic theorem for Markov chains indexed by a homogeneous tree. The entropy ergodic theorem studies the asymptotic equipartition property of information source in the information theory, and the theory of stochastic processes indexed by tree has become one of the research branches in probability theory recently. We first introduce the definition of the generalized entropy density. Then we prove the strong limit theorem of certain random variables by constructing a single parameter class of random variables with means 1 and using the Markov inequality and the Borel-Cantelli lemma. Finally, from the corollaries of the above theorem, we obtain the strong law of large numbers for the delayed average of the number of occurrences of some state and the generalized entropy ergodic theorem for finite Markov chains indexed by a Cayley tree, which generalize some known results. Related Articles | Metrics

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Preconditioned MCG Method for Complex Linear Systems ZHANG Ying-chun, LV Quan-yi, XIAO Man-yu 2018, 35 (3):  308-318.  doi: 10.3969/j.issn.1005-3085.2018.03.006 Abstract ( 211 )   PDF (174KB) ( 391 )   Save Complex linear equations have a wide application in science and engineering, and an important issue is how to solve it with high efficiency. Until now, complex linear equations are usually solved by either iteration methods or the solution of the real equations transformed from the original equations. Conjugate gradient method (CG method) is discussed from two different viewpoints, and it is proved theoretically that these two kinds of CG methods have the same convergence. Because the convergence speed of the modified conjugate gradient method (MCG method) and conjugate gradient method are essentially similar, MCG method is extended to solve complex linear equations. Besides, a preconditioned MCG method is proposed in order to improve the convergence speed. Finally, the consistency of algorithms and theoretical analysis and effectiveness of the proposed precondition algorithm are validated by numerical examples. Related Articles | Metrics

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New Construction of Perfect Gaussian Integer Sequence with Period $p^2$ KE Pin-hui, HU Dian-fen, CHANG Zu-ling 2018, 35 (3):  319-328.  doi: 10.3969/j.issn.1005-3085.2018.03.007 Abstract ( 154 )   PDF (160KB) ( 557 )   Save Due to its good correlation property, perfect Gaussian integer sequence has been widely used in modern communication system. However, the known construction methods for perfect Gaussian integer sequence is limited. In this paper, we present a new construction method for perfect Gaussian integer sequences with their period being the square of an odd prime. Based on the generalized cyclotomy of order 2 over the ring of integers with modulo being an odd prime square, we construct Gaussian integer sequence with the period being an odd prime square and determine its autocorrelation function distributions. Furthermore, the construction of perfect Gaussian integer sequence is proved to be equivalent to the solution of an equation system of degree 2 over complex field. Special cases of above equation system are then considered. Related Articles | Metrics

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Completions for Partial Inverse M-matrices of Double Cycles CHENG Fang 2018, 35 (3):  329-339.  doi: 10.3969/j.issn.1005-3085.2018.03.008 Abstract ( 166 )   PDF (151KB) ( 311 )   Save The inverse M-matrix is a class of very important nonnegative matrices, which has been widely used in many fields such as biology and physics. Using graph theory to study the completion of inverse M-matrix is an important direction in the field of inverse M-matrices. A double cycle graph is a directed graph built from two simple directed cycles intersecting at any number of vertices in structure. In this paper, we discuss the inverse M-matrix completion problem for this class of graphs. The necessary and sufficient conditions are presented for partial matrices having inverse M-matrix completions in two different cases, whose associated graphs are double cycles. The conditions are as follows: when all vertices in the double cycle graph are specified, the cycle product of each cycle is less than the product of its diagonal elements; when the vertices in the double cycle graph include unspecified vertices, each cycle contains at least one unspecified vertex. Furthermore, we present the specific completion algorithm, and the effectiveness of the algorithms is demonstrated by a numerical example. Related Articles | Metrics

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A Characterization of a Class of Arithmetic Functions YOU Li-hua, CHEN Ya-fei, YUAN Ping-zhi, SHEN Jie-qin 2018, 35 (3):  340-354.  doi: 10.3969/j.issn.1005-3085.2018.03.009 Abstract ( 136 )   PDF (120KB) ( 253 )   Save During the last decade, there have been a great deal of researches on Cauchy-like functional equation on positive integer. As we know, the arithmetic function is widely applied in the field of artificial intelligence, cryptography and engineering. This paper mainly discusses the characterization of a class of arithmetic functions. Firstly, we give a characterization under some condition, and then propose a conjecture and show that the result holds for several simple cases. Finally, we summarize the process of argument and give some valuable conclusions which have been found during the proof process. Related Articles | Metrics

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Conservation Laws and Super Hamiltonian Structures for a New Six-component Super NLS-MKdV Hierarchy WEI Han-yu, XIA Tie-cheng 2018, 35 (3):  355-366.  doi: 10.3969/j.issn.1005-3085.2018.03.010 Abstract ( 271 )   PDF (121KB) ( 502 )   Save How to construct a new super soliton equation hierarchy is an important problem in soliton theory. In this paper, based on the matrix Lie super algebras, we obtain a new six-component super NLS-MKdV hierarchy with the aid of zero curvature equation, and gain different reductions for the super integrable equations. Super trace identity is used to furnish the super Hamiltonian structures for the resulting nonlinear super integrable hierarchy. Finally, we establish infinite conservation laws for the integrable six-component super NLS-MKdV hierarchy by introducing two variables. Especially, in the process of computation, Fermi variables play an important role in super integrable systems. Related Articles | Metrics