关于周期吸附系统的分布混沌的注记

设X是一个紧致度量空间,f X→X是一个连续映射.若存在f的一个m-周期点p和另一个m'-周期点q(p≠q),使得对任意非空开集V(C)X,都有{p,q}(C)∞ Un=0fn(V),则称动力系统(X,f)是一个(m,m')型周期吸附系统.证明了:1)若(X,f)是一个(m,m')型周期吸附系统且X是自密的,则对任一给定的正整数k,存在一个fk的的分布混沌集S,使得S与X的任一非空开集之交均含有一个Cantor集;2)若(X,f)是一个(m,m')型周期吸附系统且拓扑共轭于(X ',f'),则(X ',f')也是一个(m,m')型周期吸附系统.改进和推广了已有结果.     

Inequalities for Humbert functions

This paper is motivated by an open problem of Luke’s theorem. We consider the problem of developing a unified point of view on the theory of inequalities of Humbert functions and of their general ratios are obtained. Some particular cases and refinements are given. Finally, we obtain some important results involving inequalities of Bessel and Whittaker’s functions as applications.     

Borch’s Theorem from the perspective of comonotonicity

This short note revisits the classical Theorem of Borch on the characterization of Pareto optimal risk exchange treaties under the expected utility paradigm. Our objective is to approach the optimal risk exchange problem by a new method, which is based on a Breeden–Litzenberger type integral representation formula for increasing convex functions and the theory of comonotonicity. Our method allows us to derive Borch’s characterization without using Kuhn–Tucker theory, and also without the need of assuming that all utility functions are continuously differentiable everywhere. We demonstrate that our approach can be used effectively to solve the Pareto optimal risk-sharing problem with a positivity constraint being imposed on the admissible allocations when the aggregate risk is positive.     

Bessel-type inequalities in Hilbert C *-modules

Regarding the generalizations of the Bessel inequality in Hilbert spaces which are due to Bombieri and Boas–Bellman, we obtain a version of the Bessel inequality and some generalizations of this inequality in the framework of Hilbert C *-modules.     

Controlled diffusions in a random medium

Using homogenization theory we treat the problem of controlled diffusions in a random medium with rapidly varying composition. This involves homogenization of a nonlinear Bellman dynamic programming equation wtih rapidly varying random coefficients. The appropriate "averaged form" of this equation is derived to define the limiting contrl problem; and a precise convergence result is given     

L~p CONTINUITY OF HRMANDER SYMBOL OPERATORS OpS_（0,0） ~m AND NUMERICAL ALGORITHM

If we use Littlewood-Paley decomposition, there is no pseudo-orthogonality for Ho¨rmander symbol operators OpS m 0 , 0 , which is different to the case S m ρ,δ (0 ≤δ < ρ≤ 1). In this paper, we use a special numerical algorithm based on wavelets to study the L p continuity of non infinite smooth operators OpS m 0 , 0 ; in fact, we apply first special wavelets to symbol to get special basic operators, then we regroup all the special basic operators at given scale and prove that such scale operator’s continuity decreases very fast, we sum such scale operators and a symbol operator can be approached by very good compact operators. By correlation of basic operators, we get very exact pseudo-orthogonality and also L 2 → L 2 continuity for scale operators. By considering the influence region of scale operator, we get H 1 (= F 0 , 2 1 ) → L 1 continuity and L ∞→ BMO continuity. By interpolation theorem, we get also L p (= F 0 , 2 p ) → L p continuity for 1 < p < ∞ . Our results are sharp for F 0 , 2 p → L p continuity when 1 ≤ p ≤ 2, that is to say, we find out the exact order of derivations for which the symbols can ensure the resulting operators to be bounded on these spaces.     

一类可积非哈密顿系统的极限环数目的上界

研究了一类可积非哈密顿系统的极限环的上界,利用Abel积分证明其在一类2n+1次多项式扰动下至多可以产生n+1个极限环,并且是可以实现的.     

Optimal proportional reinsurance and investment with multiple risky assets and no-shorting constraint

In this paper, the basic claim process is assumed to follow a Brownian motion with drift. In addition, the insurer is allowed to invest in a risk-free asset and n risky assets and to purchase proportional reinsurance. Under the constraint of no-shorting, we consider two optimization problems: the problem of maximizing the expected exponential utility of terminal wealth and the problem of minimizing the probability of ruin. By solving the corresponding Hamilton–Jacobi–Bellman equations, explicit expressions for their optimal value functions and the corresponding optimal strategies are obtained. In particular, when there is no risk-free interest rate, the results indicate that the optimal strategies, under maximizing the expected exponential utility and minimizing the probability of ruin, are equivalent for some special parameter. This validates Ferguson’s longstanding conjecture about the relation between the two problems.     

基于不均衡数据的小企业信用风险评价

小企业信用风险评价既是银行风险管理问题,又事关经济社会稳定。针对小企业贷款实践中,违约样本远少于非违约样本、且违约客户误判对银行影响较大的现实,采用不均衡支持向量机对小企业信用风险评价指标进行赋权,进而构建了能有效区分违约客户、非违约客户的评价模型。根据有无特定评价指标、特定评价指标数值变化对贷款小企业违约状态的影响程度赋权;反映了对违约状态影响越大、评价指标权重越大的赋权思路。将违约样本正确识别率、违约样本的准确率与查全率等因素作为支持向量机赋权模型中客户识别率的度量标准,改变了样本数据不均衡所导致的样本总体精度很高、违约样本精度反而不高的现象。研究结果表明:行业景气指数、资本固定化比率、净利润现金含量、恩格尔系数、营业利润率等评价指标对小企业信用风险的影响较大。     

Solvability of a class of boundary value problems in the space of convergent sequences

We consider two types of infinite systems of second-order differential equations with boundary conditions in the Banach sequence space c. For each system, sufficient conditions are provided for the existence of solutions. Our approach is based on the use of measure of noncompactness concept and the application of Darbo’s theorem for condensing operators. Some examples are presented to illustrate the obtained results.