两矩形上的全偏差

考虑如下极值问题的存在性和唯一性:■,其中h代表从矩形Q₁到矩形Q₂并保持端点且具有有限偏差的所有同胚映射的集合.     

{Well-posedness of degenerate differential equations with infinite delay in Holder continuous function spaces

Using operator-valued $\dot{C}^\alpha$-Fourier multiplier results on vector- valued H\"older continuous function spaces, we give a characterization for the $C^\alpha$-well-posedness of the first order degenerate differential equations with infinite delay $(Mu)"(t) = Au(t) + \int_{-\infty}^t a(t-s)Au(s)ds + f(t)$ ($t\in\R$), where $A, M$ are closed operators on a Banach space $X$ such that $D(A)\cap D(M)\neq \{0\}$, $a\in L^1_{\rm{loc}}(\R_+)\cap L^1(\mathbb{R}_+; t^\alpha dt)$.     

Budget-constrained optimal insurance with belief heterogeneity

We re-examine the problem of budget-constrained demand for insurance indemnification when the insured and the insurer disagree about the likelihoods associated with the realizations of the insurable loss. For ease of comparison with the classical literature, we adopt the original setting of Arrow (1971), but allow for divergence in beliefs between the insurer and the insured; and in particular for singularity between these beliefs, that is, disagreement about zero-probability events. We do not impose the no sabotage condition on admissible indemnities. Instead, we impose a state-verification cost that the insurer can incur in order to verify the loss severity, which rules out ex post moral hazard issues that could otherwise arise from possible misreporting of the loss by the insured. Under a mild consistency requirement between these beliefs that is weaker than the Monotone Likelihood Ratio (MLR) condition, we characterize the optimal indemnity and show that it has a simple two-part structure: full insurance on an event to which the insurer assigns zero probability, and a variable deductible on the complement of this event, which depends on the state of the world through a likelihood ratio. The latter is obtained from a Lebesgue decomposition of the insured’s belief with respect to the insurer’s belief.     

Optimal investment strategies and risk-sharing arrangements for a hybrid pension plan

A continuous time stochastic model is used to study a hybrid pension plan, where both the contribution and benefit levels are adjusted depending on the performance of the plan, with risk sharing between different generations. The pension fund is invested in a risk-free asset and multiple risky assets. The objective is to seek an optimal investment strategy and optimal risk-sharing arrangements for plan trustees and participants so that this proposed hybrid pension system provides adequate and stable income to retirees while adjusting contributions effectively, as well as keeping its sustainability in the long run. These goals are achieved by minimizing the expected discount disutility of intermediate adjustment for both benefits and contributions and that of terminal wealth in finite time horizon. Using the stochastic optimal control approach, closed-form solutions are derived under quadratic loss function and exponential loss function. Numerical analysis is presented to illustrate the sensitivity of the optimal strategies to parameters of the financial market and how the optimal benefit changes with respect to different risk aversions. Through numerical analysis, we find that the optimal strategies do adjust the contributions and retirement benefits according to fund performance and model objectives so the intergenerational risk sharing seem effectively achieved for this collective hybrid pension plan.     

基于Copula函数的华南台风灾情重现期研究

利用1981-2014年华南台风灾情数据,选取受灾人口、农作物受灾面积和直接经济损失,应用Copula函数理论,计算灾情重现期,分析台风灾害的灾情.首先,借助Clayton Copula函数构造三变量的联合分布,计算单变量重现期、联合重现期及同现重现期,并求出该重现期下的设计值.计算结果表明联合重现期的设计值要优于单变量重现期和同现重现期的设计值．因此,选取联合重现期的设计值作为防灾标准的最优参考,并将联合重现期记为灾情重现期．然后,计算2015-2017年登陆华南台风灾害的灾情重现期,并对台风灾害的灾情进行分析．发现台风灾情重现期越长的台风造成的灾情越严重．最后,利用灾情重现期与致灾重现期对台风灾害的发生频率作综合性分析,可以为台风灾害的风险评估提供一种新思路．     

Structure of Pareto optima in an infinite-horizon economy where agents have recursive preferences

This article generalizes the one-agent growth theory with discounting to the case of several agents with recursive preferences. In a multi-consumption goods world, we show that, under some regularity conditions, any Pareto optimum can be viewed as a function of a trajectory of a dynamical system. The state space can be chosen to be the product of the space of capitals and the unit simplex. We define and study the properties of generalized value functions.     

Bootstrap approximation of nearest neighbor regression function estimates

Let (X, Y) be a random vector in the plane and denote by m(x) = (Y|X = x) the corresponding regression function. We show that the bootstrap approximation for the distribution of a smoothed nearest neighbor estimate of m(x) is valid. Also we compare, by Monte Carlo, confidence intervals which are obtained from both the normal and the bootstrap approximation.     

Estimation of the Coefficient of Multiple Determination

Assume that we have iid observations on the random vector X = (X ,...,X ) following a multivariate normal distribution N (,) where both R and (p.d.) are unknown. Let denote the multiple correlation coefficient between X and (X ,...,X ). The parameter = , called the multiple coefficient of determination, indicates the proportion of variability in X explained by its best linear fit based on (X ,..., X ). In this paper we consider the point estimation of under the ordinary squared error loss function. The usual estimators (MLE, UMVUE) have complicated risk expressions and hence it is quite difficult to get exact decision-theoretic results. We therefore follow the asymptotic decision theoretic approach (as done by Ghosh and Sinha (1981, Ann. Statist., 9, 1334-1338)) and study Second Order Admissibility of various estimators including the usual ones.     

Uniform Asymptotic Expansions for Meixner Polynomials

Meixner polynomials m _n (x;β,c) form a postive-definite orthogonal system on the positive real line x > 0 with respect to a distribution step function whose jumps are Unlike classical orthogonal polynomials, they do not satisfy a second-order linear differential equation. In this paper, we derive two infinite asymptotic expansions for m _n (nα;β,c) as . One holds uniformly for , and the other holds uniformly for , where a and b are two small positive quantities. Both expansions involve the parabolic cylinder function and its derivative. Our results include all five asymptotic formulas recently given by W. M. Y. Goh as special cases. April 16, 1996. Date revised: October 30, 1996.     

Banach空间中微分包含的生存单调轨道与解的稳定性

我们在无限维空间中研究微分包含的生存W—单调轨道的存在性．基于Zorn引理，我们给出了一个逼近方法，在较弱的条件下得到了一个存在性定理，其特殊情形则包含了已有的生存定理和微分方程理论中的若干结果作为应用，我们首先研究了微分包含生存解的整体存在性，得到了整体生存理．然后我们研究了微分包含解的稳定性，得到一些新的结果．