Self-Converse Directed BIBDs with Block Size Four

A directed balanced incomplete block design (or D B(k,;v)) (X,) is called self-converse if there is an isomorphic mapping f from (X,) to (X,^–1), where ^–1={B ^–1:B} and B ^–1=(x _k ,x _{k –1},,x ₂,x ₁) for B=(x ₁,x ₂,,x _{k –1},x _k ). In this paper, we give the existence spectrum for self-converse D B(4,1;v). AMS Classification:05BResearch supported in part by NSFC Grant 10071002 and SRFDP under No. 20010004001     

Further results on large sets of disjoint group‐divisible designs with block size three and type 2n41

Large sets of disjoint group‐divisible designs with block size three and type 2ⁿ4¹ were first studied by Schellenberg and Stinson because of their connection with perfect threshold schemes. It is known that such large sets can exist only for n ≡0 (mod 3) and do exist for all odd n ≡ (mod 3) and for even n=24m, where m odd ≥ 1. In this paper, we show that such large sets exist also for n=2^k(3m), where m odd≥ 1 and k≥ 5. To accomplish this, we present two quadrupling constructions and two tripling constructions for a special large set called ^*LS(2ⁿ). © 2002 Wiley Periodicals, Inc. J Combin Designs 11: 24–35, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10032     

The Rate of Convergence for Subexponential Distributions and Densities

A distribution function F on the nonnegative real line is called subexponential if lim_x(1-F ^*n (x)/(1 - F(x)) = n for all n 2, where F ^*n denotes the nfold Stieltjes convolution of F with itself. In this paper, we consider the rate of convergence in the above definition and in its density analogue. Among others we discuss the asymptotic behavior of the remainder term R _n (x) defined by R _n (x) = 1 - F*n(x) - n(1 - F(x)) and of its density analogue r_n (x) = -(R_n (x))'. Our results complement and complete those obtained by several authors. In an earlier paper, we obtained results of the form _n(x) = O(1)f(x)R(x), where f is the density of F and R(x) = ₀ ^x (1-F(y))dy. In this paper, among others we obtain asymptotic expressions of the form R _n(x)= ₂ ⁿ R₂(x) + O(1)(-f'(x))R²(x) where f' is the derivative of f.     

Calibration of a basket option model applied to company valuation

Applying real options thinking to company valuation seems theoretically and intuitively appealing. However, the real option analogy of a single European option as well as the compound option proxy perform poorly when applied to company valuation. We therefore suggest to rework the building blocks of real option applications to corporate valuation.  We introduce a framework to delineate the distribution of the underlying asset in the risk neutral world, which is important in order to value any derivative. This is achieved by an algorithm to calibrate a basket option model using real world data of observed share prices. The fitting takes account of the class of stable distributions. The index of stability of asymmetric α stable distribution serves as an over-all parameter to characterise the specific distribution.     

Asymptotic Distribution of Nodes for Near-Optimal Polynomial Interpolation on Certain Curves in R 2

Let E\subset \Bbb R ^s be compact and let d _n ^E denote the dimension of the space of polynomials of degree at most n in s variables restricted to E . We introduce the notion of an asymptotic interpolation measure (AIM). Such a measure, if it exists , describes the asymptotic behavior of any scheme τ _n ={ \bf x _k,n } _k=1 ^dnE , n=1,2,\ldots , of nodes for multivariate polynomial interpolation for which the norms of the corresponding interpolation operators do not grow geometrically large with n . We demonstrate the existence of AIMs for the finite union of compact subsets of certain algebraic curves in R ² . It turns out that the theory of logarithmic potentials with external fields plays a useful role in the investigation. Furthermore, for the sets mentioned above, we give a computationally simple construction for ``good' interpolation schemes. November 9, 2000. Date revised: August 4, 2001. Date accepted: September 14, 2001.     

Lifetime distribution and estimation problems of consecutive-k-out-of-n:F systems

Explicit formula is given for the lifetime distribution of a consecutive-k-out-of-n:F system. It is given as a linear combination of distributions of order statistics of the lifetimes of n components. We assume that the lifetimes are independent and identically distributed. The results should make it possible to treat the parametric estimation problems based on the observations of the lifetimes of the system. In fact, we take up, as some examples, the cases where the lifetimes of the components follow the exponential, the Weibull, and the Pareto distributions, and obtain feasible estimators by moment method. In particular, it is shown that the moment estimator is quite good for the exponential case in the sense that the asymptotic efficiency is close to one.This research was partially supported by the ISM Cooperative Research Program (94-ISM-CRP-5).     

Infinitely many bound state solutions of Schrodinger-Poisson equations in $\mathbb{R}^3$

In this paper, we study a system of Schr\"odinger-Poisson equation \[ \left\{ \begin{array}{c} -\Delta u+a(x)u+K(x)\phi u=|u|^{p-2}u,\quad \quad \quad \ \ \ \ \ \ x\in \mathbb{R}^3, \-\Delta \phi=K(x)u^2,\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \ x\in \mathbb{R}^3, \end{array} \right. \] where $p\in (4,6)$ and $ K\geq (\not\equiv) 0$. Under some suitable decay assumptions but without any symmetry property on $a$ and $K$, we obtain infinitely many solutions of this system.     

Elliptic Systems with a Partially Sublinear Local Term

Let $1 0.$ This is in sharp contrast to D'Aprile and Mugnai's non-existence results.     

一类微分代数系统的受控不变分布及其不变性

针对一类非线性微分代数系统,利用M导数方法,给出了受控不变分布的概念,并讨论了此类微分代数系统受控不变分布的一些性质.给出了一个计算包含在系统输出核(kerE(h))内的最大受控不变分布的算法,同时讨论了该算法的一些性质.最后,给出一个例子说明如何利用给出的算法计算微分代数系统的包含在系统输出核内的最大受控不变分布.     

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.