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The Relations Among Various Markov Chains

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wuhan University Journal of Natural Sciences 2001年第3期6卷 643-648页

作者： hu Di\|he College of mathematics and {2.,{2. University, wuhan 430072. china wuhan University College of Mathematics and Statistics Wuhan China (GRID:grid.49470.3e) (ISNI:***)

Some basic equations and the relations among various Markov chains are established. These works are the bases in the investigation of the theory of Markov chain in random environment.

关键词： Hopf Markov chain Markov chain in random environment skew product Markov chain sample Markov chain in random environment

THE EXISTENCE AND MOMENTS OF CANONICAL BRANCHING CHAIN IN RANDOM ENVIRONMENT

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Acta Mathematica Scientia 2004年第3期24卷 499-506页

作者： huDihe TheCollegeofmathematicsandstatistics WuhanUniversityWuhan430072China

The concepts of branching chain in random environmnet and canonical branching chain in random environment are introduced. Moreover the existence of these chains is proved. Finally the exact formulas of mathematical ex... 详细信息

关键词： Random transition matrix branching chain in random environment canonical branching chains in random environments generator random varialble

*** CONTRACTION OPERATORS AND STATISTICALLY SELF-SIMILAR SETS

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Chinese Annals of mathematics,Series B 2002年第4期23卷 461-468页

作者： hu DIHECollege of mathematics and {2., {2. University, wuhan 430072. china. E-mail: dhhu@***. College of mathematics and statistics Wuhan University Wuhan 430072 China

I.i.d. random sequence is the simplest but very basic one in stochastic processes, and statistically self-similar set is the simplest but very basic one in random recursive sets in the theory of random fractal. Is there any relation between i.i.d. random sequence and statistically self-similar set? This paper gives a basic theorem which tells us that the random recursive set generated by a collection of i.i.d. statistical contraction operators is always a statistically self-similar set.

关键词： Hausdorff metric Statistical contraction operator Statistically self-similar set Statistically self-similar measure

THE CLASSIFICATION AND PERIOD OF STATES FOR MARKOV CHAIN IN RANDOM ENVIRONMENT

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Acta Mathematica Scientia 2005年第1期25卷 23-29页

作者：胡迪鹤 College of mathematics and statistics {2. University Wuhan 430072 China

This paper is a continuation of [8]. In Section 1, three kinds of communication are introdnced for two states and the relations among them are investigated. In Section 2. two kinds of period of a state are introdnced and it is obtained that the period is a 'class property',i.e. two states x and y belong to same class implies the period of x is equal to the period of y.

关键词： Markov chain in random environment recurrent state transient state period

Optimal Portfolio Selection Strategies under Some Constraints

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wuhan University Journal of Natural Sciences 2009年第4期14卷 281-286页

作者： LUO Kui,WANG Guangming,hu Yijun School of mathematics and {2.,{2. University,{2. 430072.hubei,china School of mathematics and statistics Wuhan University Wuhan 430072 Hubei China

A portfolio selection problem for any utility function is introduced, where all the market coefficients are random and the wealth process under any admissible trading strategy is not allowed to be below a benchmark wealth process. The problem is completely solved using a decomposition approach. First, the portfolio selection problem is formulated, and its feasibility is characterized. Then, the problem is decomposed to two steps to solve. After a system of equations for a Lagrange multiplier is solved, the portfolio selection problem is derived as the replicating portfolios of contingent claims. Finally, some simulations are demonstrated.

关键词： portfolio selection Lagrange multiplier stochastic differential equation Monte-Carlo simulation

A Note on the Multifractal Decomposition of Directed Graph Self Similar Sets

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wuhan University Journal of Natural Sciences 2004年第3期9卷 269-272页

作者： Zheng Shui-cao 1,2., hu Di-he 1 1. School of {2. and statistics, {2. University , {2. 430072. hubei, china 2. The Basic Teaching Department, Jimei University, Xiamen 36102., Fujian, china wuhan University School of Mathematics and Statistics Wuhan Hubei China (GRID:grid.49470.3e) (ISNI:***) Jimei University The Basic Teaching Department Xiamen Fujian China (GRID:grid.411902.f) (ISNI:***) wuhan University School of Mathematics and Statistics Wuhan Hubei China (GRID:grid.49470.3e) (ISNI:***)

We investigated the directed graph self similar sets under some weak overlapping condition. We get the multifractal decomposition formulas for these sets, i. e., dimK u a =DimK u a =f(a), wheref is the multifractal spectral function of the directed graph self similar measure, Especially, the results improve that of Edgar and Mauldin to the case which allows certain overlapping. Key words Hausdorff dimension - Hausdorff measure - multifractal decomposition CLC number O 2.1. 6 Foundation item: Supported by the National Natural Science Foundation of china (10371092. and the Foundation of wuhan UniversityBiography: Zheng S{2.i-cao (1973-), male, Ph. D candidate, research direction: stochastic processes and random fractals.

关键词： Hausdorff dimension Hausdorff measure multifractal decomposition

UNIFORM ESTIMATE ON FINITE TIME RUIN PROBABILITIES WITH RANDOM INTEREST RATE

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Acta Mathematica Scientia 2010年第3期30卷 688-700页

作者：明瑞星何晓霞胡亦钧刘娟 School of mathematics and Information Sciences Jiangxi Normal University School of mathematics and statistics Wuhan University College of Science Wuhan University of Science and Technology College of mathematics and statistics Hubei Normal University

We consider a discrete time risk model in which the net payout （insurance risk） {Xk, k = 1, 2....} are assumed to take real values and belong to the heavy-tailed class L∩ D and the discount factors （financial risk） {Yk, k = 1,2....} concentrate on [θ, L], where 0 〈 0 〈 1, L 〈 ∞, {Xk, k = 1,2....}, and {Yk, k=1,2....} are assumed to be mutually independent. We investigate the asymptotic behavior of the ruin probability within a finite time horizon as the initial capital tends to infinity, and figure out that the convergence holds uniformly for all n ≥ 1, which is different from Tang Q H and Tsitsiashvili G （Adv Appl Prob, 2.04, 36： 12.8-12.9）.

关键词： Random interest rate finite time ruin probability uniformity

OPTIMAL PROPORTIONAL REINSURANCE WITH CONSTANT DIVIDEND BARRIER

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Acta Mathematica Scientia 2010年第3期30卷 791-798页

作者：袁海丽胡亦钧 School of mathematics and statistics Wuhan University

In this article, we consider an optimal proportional reinsurance with constant dividend barrier. First, we derive the Hamilton-Jacobi-Bellman equation satisfied by the expected discounted dividend payment, and then get the optimal stochastic control and the optimal constant barrier. Secondly, under the optimal constant dividend barrier strategy, we consider the moments of the discounted dividend payment and their explicit expressions are given. Finally, we discuss the Laplace transform of the time of ruin and its explicit expression is also given.

关键词： Stochastic control constant barrier time of ruin expected discounted dividend payment moments Laplace transform of the time of ruin

Multifractal Decomposition of Statistically Self-Similar Sets

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Acta Mathematica Sinica,English Series 2001年第3期17卷 507-516页

作者： Jing hu YU wuhan Institute of Physics and {2.,The Chinese Academy of Sciences,wuhan 430071,P.R.china E-mail:ding@wipm.whcnc.ac.cnDi He hu College of {2. and statistics.wuhan University,wuhan 430072.P.R.china E-mail:dhhu@*** wuhan Institute of Physics and mathematics The Chinese Academy of Sciences Wuhan 430071 P. R. China College of mathematics and statistics Wuhan University Wuhan 430072 P. R. China

Let K be a statistically self-similar set defined by *** this paper,we construct a random measure ρ which is supported by K and study the multifractal decomposition for K with p. Under such a decomposition,we obtain ... 详细信息

关键词： Statistically self-similar sets Multifractal decomposition Spectrum function