JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)

Pricing of power options based on Tsallis distribution and O-U process

ZHAO Pan, XIAO Qing-xian

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(04): 1-7. doi:10.6040/j.issn.1671-9352.0.2014.160

Abstract ( 1543 )

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Characteristics of fat-tail, long-term dependence of return distribution and mean reversion of asset prices were considered. Thus, the distribution of Tsallis entropy, which has fat-tailed and long-term dependent characteristics, and O-U process were selected to describe the law of the asset prices movement. By using the stochastic differential and martingale, the pricing of power European options was studied. The pricing formulas of power European call and put options, under the asset prices following the maximum Tsallis entropy distribution, were obtained, and the formulas not only generalize the classical Black-Scholes' conclusion, but also contain the conclusions in the other literatures.

Lifetime distribution behavior of discrete open censored δ-shock model

YE Jian-hua, MA Ming

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(04): 8-13. doi:10.6040/j.issn.1671-9352.0.2014.240

Abstract ( 1761 )

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The δ-shock model is an important shock model in reliability theory which has potential applications in various fields such as insurance, traffic and relationship marketing. The discrete open censored δ-shock model was presented. The lifetime behavior of the discrete open censored δ-shock model that shock interarrival times follow lattice distribution was studied. And the probability distribution and the expectation of the system lifetime were obtained for all the failure critical values. In particular, as a corollary, the lifetime distribution was obtained when the interarrival times follow a geometric distribution, i.e. the binomial process.

Complete moment convergence for sequences of φ mixing random variables

ZHENG Lu-lu, GE Mei-mei, LIU Yan-fang, WANG Xue-jun

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(04): 14-19. doi:10.6040/j.issn.1671-9352.0.2014.177

Abstract ( 1528 )

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Under some suitable moment conditions, the complete moment convergence for sequences of φ-mixing random variables was investigated by using the moment inequality of φ-mixing random variables and the truncated method. The result obtained in this paper extends the corresponding ones for independent random variables and φ-mixing random variables. In addition, the complete convergence is improved to complete moment convergence.

Maximum empirical likelihood estimation in nonlinear semiparametric regression models with missing data

WU Da-yong, LI Feng

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(04): 20-23. doi:10.6040/j.issn.1671-9352.0.2014.043

Abstract ( 1635 )

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The linear semiparametric regression models with missing data were considered. The maximum empirical estimations of the regression coefficients, and the smoothing function were obtained by the maximum empirical method. The asymptotic normality and consistency of the proposed estimations were proved under some appropriate conditions.

An important application and estimation of Levy mean

ZHAI Xue-bo, HU Xiu-yan

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(04): 24-26. doi:10.6040/j.issn.1671-9352.0.2014.102

Abstract ( 1199 )

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The theory of optimal reconstruction is an important part of computational complexity, and the estimations of Levy mean are widely used in the study of the optimal recovery problems. An important estimation of Levy mean in L_p spaces with 0<p<∞ was obtained. As an application of this result on the space of spherical polynomials, there exists a spherical polynomial such that the norms are equivalent for 2≤p <∞ under some conditions.

Controllability and observability of k-valued control networks

DENG Lei, ZHAO Jian-li, LIU Hua, LI Ying

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(04): 27-35. doi:10.6040/j.issn.1671-9352.0.2014.162

Abstract ( 1446 )

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By using the method of semi-tensor product of matrices, the controllability and observability of k-valued control networks were investigated. Controllability matrix was constructed by eigenfunction and a novel necessary and sufficient condition for controllability was given. The new conditions simplify computational complexity of original conditions,and the highest power of matrix is reduced from k^n+m to kⁿ. Aslo, a sufficient condition for observabilitywas obtained, which can be computed easily.

A one-to-one correspondence between fuzzy G-ideals and fuzzy Galois connections on fuzzy complete lattices

SHEN Chong, YAO Wei

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(04): 36-41. doi:10.6040/j.issn.1671-9352.0.2014.482

Abstract ( 1468 )

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This paper deals with fuzzy G-ideals on fuzzy complete lattices. Firstly, the concept of fuzzy G-ideals is defined and it is proved that the set of all fuzzy G-ideals of X×Y is a fuzzy complete lattice with respect to fuzzy in clusion order. Secondly, by making use of the intrinsic fuzzy inclusion orders on fuzzy G-ideals, the relationship between fuzzy Galois connections and fuzzy G-ideals is studied. It is shown that the fuzzy poset of fuzzy Galois connections between fuzzy complete lattices X and Y is order-isomorphic to the fuzzy poset of all fuzzy G-ideals of X×Y.

Existence and uniqueness of solutions for nonlinear fractional four-point boundary value problems

CHEN Qiang, JIA Mei, ZHANG Hai-bin

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(04): 42-48. doi:10.6040/j.issn.1671-9352.0.2014.157

Abstract ( 1484 )

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This paper investigates existence and uniqueness of solutions for a type of four-point boundary value problems with fractional order differential equation.By using the Schauder fixed point theorem and the Banach contraction principle,we obtain the sufficient conditions of the existence and uniqueness of solutions for the nonlinear fractional four-point boundary value problems.

Symmetry, reductions and exact solutions of the (2+1)-dimension Caudrey-Dodd-Gibbon equation

LIU Yong, LIU Xi-qiang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(04): 49-55. doi:10.6040/j.issn.1671-9352.0.2014.175

Abstract ( 1556 )

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Using the classical Lie group method, we find the classical symmetry and reductions of (2+1)-dimensional Caudrey-Dodd-Gibbon(CDG for short) equation. At the same time, a great many of solutions are derived by solving the reduction equations, including the rational functions, hyperbolic functions, trigonometric functions, and Jacobi elliptic function solutions.

Existence of the solutions for a type of nonlocal boundary value problems for fractional differential equations with p-Laplacian operator

YANG Hao, LIU Xi-ping, WU Gui-yun

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(04): 56-62. doi:10.6040/j.issn.1671-9352.0.2014.135

Abstract ( 1842 )

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In this paper, we investigate a type of nonlocal boundary value problems for fractional differential equations with p-Laplacian operator. By means of Schauder fixed point theorem, the existence of the solutions for the boundary value problems are obtained.

Adjacent vertex-distinguishing edge/total colorings of double graph of some graphs

HE Xue, TIAN Shuang-liang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(04): 63-66. doi:10.6040/j.issn.1671-9352.0.2014.327

Abstract ( 1586 )

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Let G be a simple graph with vertex set V(G) and edge set E(G). An edge-coloring σ of G is called an adjacent vertex distinguishing edge-coloring of G if C_σ(u)≠C_σ(v) for any uv∈E(G), where C_σ(u) denotes the set of colors of edges incident with u. A total-coloring σ of G is called an adjacent vertex distinguishing total-coloring of G if S_σ(u)≠S_σ(v) for any uv∈E(G), where S_σ(u) denotes the set of colors of edges incident with u together with the color assigned to u. The minimum number of colors required for an adjacent vertex-distinguishing edge-coloring (resp. total-coloring) of G is called adjacent vertex-distinguishing edge (resp. total) chromatic number, and denoted by χ'_as(G) (resp. χ_at(G)). The upper bounds for these parameters of the double graph D(G) of graph G are given in this paper. Specifically, the exact value of these parameters for the double graph of complete graphs and trees are determined.

A class of quasi-Armendariz subrings of matrix rings over reduced rings

ZHANG Wan-ru, GUO Jin-sheng

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(04): 67-70. doi:10.6040/j.issn.1671-9352.0.2014.310

Abstract ( 1406 )

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A class of special quasi-Armendariz subrings S_n(R) of the n×n matrix ring M_n(R) over a reduced ring is investigated. It is shown that S_n(R) is a quasi-Armendariz ring if R is a reduced ring with compatible endomorphisms α₂,…,α_n.

The presented dimensions of polynomial rings

GUO Ying, YAO Hai-lou

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(04): 71-75. doi:10.6040/j.issn.1671-9352.0.2014.416

Abstract ( 1574 )

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Let R be a ring with a unit element, and M be a right R-Module. The relationship between FPd(M_R) and FPd(M_R[x]) as well as between FPD(R) and FPD(R[x]) are obtained by using the presented dimensions of polynomial rings, when R and R[x] are coherent rings.

On Ore extensions of nilpotent p.p.-rings and nilpotent Baer rings

WANG Yao, ZHANG Jiu-lin, REN Yan-li

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(04): 76-81. doi:10.6040/j.issn.1671-9352.0.2014.494

Abstract ( 1557 )

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The nilpotent p.p., nilpotent Baer and weak McCoy property of the Ore extensions of a ring are investigated. Let R be a quasi-IFP and (α,δ)-condition ring. It is mainly shown that (1) if R is a nilpotent p.p.-ring, then R[x;α,δ] is a nilpotent p.p.-ring; (2) if R is a nilpotent Baer ring, then R[x;α,δ] is a nilpotent Baer ring; (3) R[x;α,δ] is a weak McCoy ring.

The Riordan group and symmetric lattice paths

DENG Li-hua, DENG Yu-ping, Louis W. Shapiro

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(04): 82-89. doi:10.6040/j.issn.1671-9352.0.2014.196

Abstract ( 1436 )

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The symmetric lattice paths are studied. Let d_n, m_n, and s_n denote the number of symmetric Dyck paths, symmetric Motzkin paths, and symmetric Schröder paths of length 2n, respectively. By using Riordan group methods, six identities relating d_n, m_n, and s_n are obtained and also two of them combinatorial proofs are given. Finally, some relations satisfied by the generic element of some special Riordan arrays are investigated and the average mid-height and the average number of points on the x-axis of symmetric Dyck paths of length 2n are obtained.

The new properties of core inverse of matrices

LUO Gao-jun, ZUO Ke-zheng, ZHOU Liang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(04): 90-94. doi:10.6040/j.issn.1671-9352.0.2014.403

Abstract ( 1491 )

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Several new properties and characteristics of core inverse,the necessary and sufficient conditions of core inverse are given by the decomposition of Σ-K-L of the matrix.

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