THE CLASSIFICATION OF NILPOTENT LEIBNIZ 3-ALGEBRAS

The notions of the nilpotent and the strong-nilpotent Leibniz 3-algebras are defined. And the three dimensional two-step nilpotent, strong-nilpotent Leibniz 3-algebras are classified.     

Asymptotic theory for the empirical Haezendonck–Goovaerts risk measure

Haezendonck–Goovaerts risk measures is a recently introduced class of risk measures which includes, as its minimal member, the Tail Value-at-Risk (T-VaR)—T-VaR arguably the most popular risk measure in global insurance regulation. In applications often one has to estimate the risk measure given a random sample from an unknown distribution. The distribution could either be truly unknown or could be the distribution of a complex function of economic and idiosyncratic variables with the complexity of the function rendering indeterminable its distribution. Hence statistical procedures for the estimation of Haezendonck–Goovaerts risk measures are a key requirement for their use in practice. A natural estimator of the Haezendonck–Goovaerts risk measure is the Haezendonck–Goovaerts risk measure of the empirical distribution, but its statistical properties have not yet been explored in detail. The main goal of this article is to both establish the strong consistency of this estimator and to derive weak convergence limits for this estimator. We also conduct a simulation study to lend insight into the sample sizes required for these asymptotic limits to take hold.     

Detecting stock market regimes from option prices

Equity market returns alternate between periods of calm and crises. Researchers commonly employ regime switching models to capture this behaviour. We show that forward-looking information extracted from option prices improves regime detection. In particular, horizon spreads in option-implied equity risk premia allow earlier detection of regime switches and improve prediction of the equity premium. This findings holds across recent disaster periods like the 2008/2009 financial crisis and the 2020 Covid pandemic outbreak, in both US and Emerging equity markets.     

ZnO-SnO2透明导电薄膜的制备及性能研究

采用二步成胶工艺制备ZnO-SnO₂透明导电薄膜,应用X射线衍射、原子力显微镜、紫外-可见分光光度计、薄膜分析仪及四探针仪等对薄膜的结构、表面微观形貌、透过率和导电性能进行表征.结果表明,锌锡摩尔比为9/12,退火温度为500 ℃时,薄膜的透过率达90%,电阻率为3.15×10-3 Ω·cm.与其它工艺相比,二步成胶工艺所制备出的ZnO-SnO₂透明导电薄膜性能优异.     

指数保费准则下的最优投资和比例再保险

该文研究了保险公司的最优投资和比例再保险问题,其中假定保险公司的盈余过程为一个带扩散扰动的经典风险过程.假定再保险的保费按照指数保费原理来计算,这使得所研究的随机控制问题成为非线性的.该文同时考虑了最大化终端财富指数效用和最大化调节系数两类问题,并给出了最优值函数和相应的最优策略的解析表达.此外,该文还分析了再保险公司的风险厌恶和保险公司的不确定性参数对最优策略的影响.     

一种亚式风格可重置执行价格期权设计

本文设计了一种亚式风格的可重置执行价格期权;严格证明了可重置执行边界的存在性,以及连续区域与重置区域的单连通性;利用Hartman-Watson分布,写出了可重置期权的定价公式,并利用此公式给出了可重置执行边界的一种新的数值算法.     

Multivariate reinsurance designs for minimizing an insurer’s capital requirement

This paper investigates optimal reinsurance strategies for an insurer with multiple lines of business under the criterion of minimizing its total capital requirement calculated based on the multivariate lower-orthant Value-at-Risk. The reinsurance is purchased by the insurer for each line of business separately. The premium principles used to compute the reinsurance premiums are allowed to differ from one line of business to another, but they all satisfy three mild conditions: distribution invariance, risk loading and preserving the convex order, which are satisfied by many popular premium principles. Our results show that an optimal strategy for the insurer is to buy a two-layer reinsurance policy for each line of business, and it reduces to be a one-layer reinsurance contract for premium principles satisfying some additional mild conditions, which are met by the expected value principle, standard deviation principle and Wang’s principle among many others. In the end of this paper, some numerical examples are presented to illustrate the effects of marginal distributions, risk dependence structure and reinsurance premium principles on the optimal layer reinsurance.     

Kernel-type estimator of the reinsurance premium for heavy-tailed loss distributions

In this paper, we generalize the classical estimator of the reinsurance premium for heavy-tailed loss distributions with a kernel-type estimator. Since this estimator exhibits a bias, we propose its bias-reduced version by using a least-squares method. The asymptotic normality of the proposed estimators is established under suitable assumptions. A small simulation study is carried out to prove the performance of our approach.     

中国资本市场价值溢价与CAPM实证研究

以1995年7月-2005年12月我国证券市场深沪两市的上市公司为样本,考察了价值溢价随规模变化的规律,并检验了CAPM能否解释价值溢价以及与权益帐面市值比B/M(或规模)无关的贝塔(β)能否与股票的平均收益相补偿.实证检验发现:1)中国股市存在一定程度的价值溢价,尤其是小规模(Size)价值股在平均收益上存在着明显的价值溢价,而大规模(Size)价值股则不存在价值溢价现象;2)CAPM能够解释我国股市从1995年7月至2005年12月期间的价值溢价.从CAPM对由不同规模(Size)和B/M构造的6个组合的回归结果来看,相对于贝塔(β)为常数情况下,允许贝塔(β)的每年变化会略微增加CAPM对平均收益能力的解释能力;3)在我国股市上,只有与B/M(或规模)有关的贝塔(β)才能解释股票的收益,而与B/M(或规模)无关的贝塔(β)则不能解释股票的收益.     

手性碳量子点的制备及其应用

手性碳量子点(CQDs)因兼具优异的荧光性质、良好的生物相容性、较低的毒性、易于功能化以及手性特征等,在催化、检测和生物医学等领域具有广阔的应用潜力。目前,通过一步法或两步法制备的手性CQDs,已应用于手性催化、手性检测、高尔基体靶向成像、选择性调控酶和蛋白活性、选择性调控细胞能量代谢和促进植物生长等领域。然而,手性CQDs的发展初露头角,需进一步完善可控合成工艺,制备高荧光量子产率的长波长手性CQDs,使其在生物医学等领域绽放异彩。