Łukasiewicz Tribes are Absolutely Sequentially Closed Bold Algebras

We show that each sequentially continuous (with respect to the pointwise convergence) normed measure on a bold algebra of fuzzy sets (Archimedean MV-algebra) can be uniquely extended to a sequentially continuous measure on the generated ukasiewicz tribe and, in a natural way, the extension is maximal. We prove that for normed measures on ukasiewicz tribes monotone (sequential) continuity implies sequential continuity, hence the assumption of sequential continuity is not restrictive. This yields a characterization of the ukasiewicz tribes as bold algebras absolutely sequentially closed with respect to the extension of probabilities. The result generalizes the relationship between fields of sets and the generated -fields discovered by J. Novák. We introduce the category of bold algebras and sequentially continuous homomorphisms and prove that ukasiewicz tribes form an epireflective subcategory. The restriction to fields of sets yields the epireflective subcategory of -fields of sets.     

Minimal Martingale Measures for Discrete-time Incomplete Financial Markets

Abstract In this note, we give a characterization of the minimal martingale measure for a general discrete-time incomplete financial market.Then we concretely work out the minimal martingale messure for a specificdiscrete-time market model in which the assets'returns in different times are independent.     

Young measures generated by a class of integrands: a narrow epicontinuity and applications to Homogenization

Given a subset E of convex functions from into which satisfy growth conditions of order p>1 and an open bounded subset of , we establish the continuity of a map μΦ_μ from the set of all Young measures on equipped with the narrow topology into a set of suitable functionals defined in and equipped with the topology of Γ-convergence. Some applications are given in the setting of periodic and stochastic homogenization.     

Hessian Measures III

In this paper, we continue previous investigations into the theory of Hessian measures. We extend our weak continuity result to the case of mixed k-Hessian measures associated with k-tuples of k-convex functions, on domains in Euclidean n-space, k=1,2,…,n. Applications are given to capacity, quasicontinuity, and the Dirichlet problem, with inhomogeneous terms, continuous with respect to capacity or combinations of Dirac measures.     

A variational problem determined by probability measures

ABSTRACT

An optimization problem of maximizing an integral of a function over a family of probability measures is considered. The problem is a generalization of a well-studied variational problem in mathematical economics, concerning optimal allocations. The specific generalization that we examine arises also in the limit of singularly perturbed optimal control problems. We examine the mathematical problem and allude to the singular perturbation motivation.     

Optimal intervention under stress scenarios: A case of the Korean financial system

We consider optimal intervention methods under budget constraints when financial systems face economic shocks. We propose two policies formulated by mixed-integer linear programs where regulators inject cash into institutions. One is to minimize systemic losses, and the other is to minimize the number of defaulting institutions. Using publicly available data on the Korean financial system, we construct its entire network and apply stress scenarios to the system to compare the performances of intervention strategies and derive insights on their workings.     

Conditional tail risk measures for the skewed generalised hyperbolic family

This paper deals with the estimation of loss severity distributions arising from historical data on univariate and multivariate losses. We present an innovative theoretical framework where a closed-form expression for the tail conditional expectation (TCE) is derived for the skewed generalised hyperbolic (GH) family of distributions. The skewed GH family is especially suitable for equity losses because it allows to capture the asymmetry in the distribution of losses that tends to have a heavy right tail. As opposed to the widely used Value-at-Risk, TCE is a coherent risk measure, which takes into account the expected loss in the tail of the distribution. Our theoretical TCE results are verified for different distributions from the skewed GH family including its special cases: Student-t, variance gamma, normal inverse gaussian and hyperbolic distributions. The GH family and its special cases turn out to provide excellent fit to univariate and multivariate data on equity losses. The TCE risk measure computed for the skewed family of GH distributions provides a conservative estimator of risk, addressing the main challenge faced by financial companies on how to reliably quantify the risk arising from the loss distribution. We extend our analysis to the multivariate framework when modelling portfolios of losses, allowing the multivariate GH distribution to capture the combination of correlated risks and demonstrate how the TCE of the portfolio can be decomposed into individual components, representing individual risks in the aggregate (portfolio) loss.     

防止温度应力下海底管线发生整体屈曲的工程措施研究

为减小油气输送难度和避免原油固化,石油、天然气通常在高温高压下输送．输送过程中的高温和高压导致海底管线中产生较大的附加应力,附加应力的不断累积造成管线发生整体屈曲．对于埋地的海底管线通常会产生竖向屈曲大变形而影响使用甚至破坏．因此,需对有可能产生整体屈曲的管线采取工程防护措施．结合我国海洋工程中管线常用的铺设及保护措施,对处于保护状态下管线由温度应力引起的整体屈曲特性进行理论分析和数值推导,对沟槽保护、沟槽掩埋保护以及压块保护措施的有效性进行了系统分析和对比．     

新课标体系下高师本科数学分析教学所面临的问题和所采取的措施

从三个方面讨论了在高中新课标体系下高师本科数学分析教学所面临的问题,并结合作者的实际教学经验给出了一些具有实际操作意义的解决措施和办法.     

Multi-scale Young measures

We introduce multi-scale Young measures to deal with problems where multi-scale phenomena are relevant. We prove some interesting representation results that allow the use of these families of measures in practice, and illustrate its applicability by treating, from this perspective, multi-scale convergence and homogenization of multiple integrals.