实时定期人寿保险的破产模型及破产概率的计算

研究定期人寿保险中破产风险问题。建立了该类问题的数学模型,并分析其结构特征,推导破产概率的计算公式,并设计其计算方法。同以往模型相比,新模型的建立考虑了初始准备金的利息积累和任何时刻的新投保人的加入,采用了新的分组方式。这种新模型更加真实地刻画了实际过程,保证了传统模型中常用的某些假设得到了满足。     

Sparre Andersen模型中破产概率的边界

研究在Andersen Spaxre模型中,当破产概率的初始边界已知的时候,根据更新方程和更新方程中函数的单调性来改进破产概率的边界,并进一步改进了严重损失函数G（x,y）的边界．     

Precise rates in the law of the logarithm for the moment convergence in Hilbert spaces

Let （X, Xn; n ≥1） be a sequence of i.i.d, random variables taking values in a real separable Hilbert space （H, ｜｜·｜｜） with covariance operator ∑. Set Sn = X1 ＋ X2 ＋ ... ＋ Xn, n≥ 1. We prove that, for b 〉 -1,
lim ε→0 ε^2（b＋1） ∞ ∑n=1 （logn）^b/n^3/2 E{｜｜Sn｜｜-σε√nlogn}=σ^-2（b＋1）/（2b＋3）（b＋1） B｜｜Y｜^2b＋3
holds if EX=0,and E｜｜X｜｜^2（log｜｜x｜｜）^3bv（b＋4）〈∞ where Y is a Gaussian random variable taking value in a real separable Hilbert space with mean zero and covariance operator ∑, and σ^2 denotes the largest eigenvalue of ∑.     

Instance-optimality in probability with an -minimization decoder

Let Φ(ω), ωΩ, be a family of n×N random matrices whose entries _i,j are independent realizations of a symmetric, real random variable η with expectation and variance . Such matrices are used in compressed sensing to encode a vector by y=Φx. The information y holds about x is extracted by using a decoder . The most prominent decoder is the ℓ₁-minimization decoder Δ which gives for a given the element which has minimal ℓ₁-norm among all with Φz=y. This paper is interested in properties of the random family Φ(ω) which guarantee that the vector will with high probability approximate x in to an accuracy comparable with the best k-term error of approximation in for the range kan/log₂(N/n). This means that for the above range of k, for each signal , the vector satisfies

with high probability on the draw of Φ. Here, Σ_k consists of all vectors with at most k nonzero coordinates. The first result of this type was proved by Wojtaszczyk [P. Wojtaszczyk, Stability and instance optimality for Gaussian measurements in compressed sensing, Found. Comput. Math., in press] who showed this property when η is a normalized Gaussian random variable. We extend this property to more general random variables, including the particular case where η is the Bernoulli random variable which takes the values with equal probability. The proofs of our results use geometric mapping properties of such random matrices some of which were recently obtained in [A. Litvak, A. Pajor, M. Rudelson, N. Tomczak-Jaegermann, Smallest singular value of random matrices and geometry of random polytopes, Adv. Math. 195 (2005) 491–523].     

On the characterization of strong convergence of an iterative algorithm for a class of multi-valued variational inclusions

This paper introduces an Ishikawa type iterative algorithm for finding approximating solutions of a class of multi-valued variational inclusion problems. Characterization of strong convergence of this iterative method is established. L. C. Ceng’s research partially supported by the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions of MOE, China and the Dawn Program Foundation in Shanghai. S. Schaible’s research partially supported by the National Science Council of Taiwan. This research was partially supported by the grant NSC 96-2628-E-110-014-MY3.     

Bayesian estimation of finite time ruin probabilities

In this paper, we consider Bayesian inference and estimation of finite time ruin probabilities for the Sparre Andersen risk model. The dense family of Coxian distributions is considered for the approximation of both the inter‐claim time and claim size distributions. We illustrate that the Coxian model can be well fitted to real, long‐tailed claims data and that this compares well with the generalized Pareto model. The main advantage of using the Coxian model for inter‐claim times and claim sizes is that it is possible to compute finite time ruin probabilities making use of recent results from queueing theory. In practice, finite time ruin probabilities are much more useful than infinite time ruin probabilities as insurance companies are usually interested in predictions for short periods of future time and not just in the limit. We show how to obtain predictive distributions of these finite time ruin probabilities, which are more informative than simple point estimations and take account of model and parameter uncertainty. We illustrate the procedure with simulated data and the well‐known Danish fire loss data set. Copyright © 2009 John Wiley & Sons, Ltd.     

对数伽玛分布与负对数伽玛分布的条件概率封闭性

设X服从以α和λ为参数的对数伽玛分布或负对数伽玛分布,V服从以β为参数的负幂分布,则在X相似文献   

Molecular dynamics simulations of p-tert-butylcalix[4]arene with small guest molecules

Classical molecular dynamics simulations were used to study p-tert-butylcalix[4]arene inclusion compounds with xenon, nitrogen, hydrogen, methane, and sulfur dioxide guest molecules. The calixarene units were taken to be rigid and the intermolecular molecular interactions were modeled as a sum of the van der Waals interactions with parameters from the AMBER force field and electrostatic interactions. Simulations of the high-density alpha phase and low-density beta0 phase of p-tert-butylcalix[4]arene were used to test the force field. The predicted densities of the two phases were found to agree with experimental measurements at 173 K to within 5 %. Simulations were performed with guests placed inside the calixarene cages of the beta0 phase. Guest-host ratios of 1:1 to 1:4 were considered. Changes in the unit-cell volume and density of the phases with the addition of guest molecules and the inclusion energies for the guests were determined. Finally, the dynamics of the guest motion inside the cages were characterized by determining the root-mean-square displacements and velocity autocorrelation functions of the xenon and nitrogen guests.     

Protonated Bis(quinuclidine) Included in Channel Thiourea-Bromide and Ribbons Thiourea-Iodide Lattice: New Thiourea Inclusion Compounds

Host-guest supramolecular complexes are of special interest for understanding the chemistry in low dimensional spaces. The molecular recognition involved in the formation of such structures sometimes may be a relevant model for the kind of organized system usually found in living organisms. Matrix effects and anisotropic features which are habitual of the chemistry in restricted spaces also appear as useful for the development of new material of scientific and technological importance (Takemoto and Sonoda, 1984). Urea and thiourea clathrates constitute interesting systems in which the matrix being structured by hydrogen bond interactions has a relatively high liability to structural changes caused by the interaction with the host (Lehn, 1996). The syntheses and crystal structure of two novel ternary inclusion compounds having protonated bis (quinuclidine) as a guest into anionic thiourea-bromide and thiourea-iodide hosts are reported: (thiourea₂[quinuclidine₂H]⁺Br^?), 1 and (thiourea₂[(quinuclidine₂H)⁺]₂(I^?)₂), 2. In the two structures thiourea molecules interact with each other via N–H....S hydrogen bonds to produce ribbon-like arrangements. In structure 1 these ribbons do not contain the halogen and define two non intersecting sets running along the a and b axis, linked through N–H....Br hydrogen bonds having the external halide ions as acceptors. This ribbon-crossover defines a channel structure along c with a cavity cross section of ca. 5.85 × 15.50 Å. In structure 2, ribbons contain iodide anions as well, bridging thiourea dimers into parallel 1D structures which align their flat side parallel to the (110) set of planes leaving a free spacing of ca. 8.25 Å.     

Structure and Stability of Endohedral Complexes X@（HBNH）12

Using quantum chemistry methods B3LYP/6-31＋＋G（d,p） to optimize endohedral complexes X@（HBNH）12 （X=Li^0/＋, Na^0/＋, K^0/＋, Be^0/2＋, Mg^0/2＋, Ca^0/2＋, H and He）, the geometries with the lowest energy were achieved. Inclusion energy, standard equilibrium constant, natural charge, spin density, ionization potentials, and HOMO-LUMO energy gap were also discussed. The calculation predicted that X=Na^0/＋, K^0/＋, Mg^0/2＋, Ca^0/2＋, H and He are nearly located at the center of （HBNH）12 cluster. Li^＋ lies in less than 0.021 nm departure from the center. Li and Be^0/2＋ dramatically deviate from the center. （HBNH）12 prefers to enclose Li^＋, Be^2＋, Mg^2＋, and Ca^2＋ in it than others. Moreover, M@（HBNH）12 （M=Li, Na, K） species are ＂superalkalis＂ in that they possess lower first ionization potentials than the Cs atom （3.9 eV）.