The Discounted Moments of the Surplus After the Last Innovation Before Ruin Under the Dual Risk Model

□ This article's focus is on finding an explicit form of the discounted moments of the surplus at the time of the last jump before ruin for the compound Poisson dual risk model. For this purpose, we derive a non-homogeneous integro-differential equation, which is satisfied by the targeted quantity. To solve this equation, the general solution of the corresponding homogeneous equation and a particular solution of the non-homogeneous equation are obtained. Also, some additional results are provided, such as the defective distribution of the time to ruin and the Laplace transform of the time when the last jump before ruin happens.     

基于Levy-GARCH模型的上证50ETF市场跳跃行为与波动特征研究

上证ETF50期权的发行推动学界开始关注其标的资产的波动特点。本文引入带跳跃的Levy-GARCH非高斯条件异方差模型，结合Fourier数值极大似然估计及回溯测试，对上证50ETF的跳跃和波动特征进行实证分析，并与上证综指、深证成指进行比较。研究结果表明，与国内主要市场指数相比，上证50ETF市场同样存在显著的条件异方差效应和随机跳跃行为，但波动率并不存在显著的杠杆效应。本文通过与多个市场和行业指数进行对照比较，并从行业特征、成份股特征、市场机制特点等角度解释了上证50ETF杠杆效应不显著的原因。     

浅析当代男子优秀三级跳远运动员三跳比例

本文以具有当今世界水平男子优秀三级跳远选手的比赛成绩为依据,运用不同时期三级跳远最佳三跳组合的模式,研究了三级跳远成绩与三跳比例的关系,找出了影响不同类型运动员三级跳远比例及成绩的主要优势因素,论述了三级跳远运动员应有不同的中心训练任务和训练方法。     

HJM框架下服从跳跃扩散过程的利率模型

由于一些不可预测的随机事件的影响,纯粹的连续扩散过程难以正确描述利率变动的行为。因此,在HJM框架下,给出了服从跳跃扩散过程的利率期限结构模型,进而推导出我国固定收益市场的债券定价公式,为投资者进行投资和风险管理提供帮助。     

Learning a multivariate Gaussian mixture model with the reversible jump MCMC algorithm

This paper is a contribution to the methodology of fully Bayesian inference in a multivariate Gaussian mixture model using the reversible jump Markov chain Monte Carlo algorithm. To follow the constraints of preserving the first two moments before and after the split or combine moves, we concentrate on a simplified multivariate Gaussian mixture model, in which the covariance matrices of all components share a common eigenvector matrix. We then propose an approach to the construction of the reversible jump Markov chain Monte Carlo algorithm for this model. Experimental results on several data sets demonstrate the efficacy of our algorithm.     

矩形微通道内滑移区气体流动换热的数值模拟

在等壁温边界条件下对矩形微细通道速度滑移区的对流换热进行了二维数值模拟、在一阶速度滑移和温度跳跃的边界条件下，计算出了通道内的速度和温度以及压力分布。比较了不同克努森数Kn对于滑移速度和跳跃温度的影响。结果表明，由于气体的稀薄性，压力呈现更加线性化减小的趋势，随着Kn的增加，通道入口与出口处的滑移速度和跳跃温度至现增加的趋势。在通道入口附近，气流速度和温度变化剧烈，而在出口处截面平均流速和温度随加的增加而降低．     

Exact and efficient Bayesian inference for multiple changepoint problems

We demonstrate how to perform direct simulation from the posterior distribution of a class of multiple changepoint models where the number of changepoints is unknown. The class of models assumes independence between the posterior distribution of the parameters associated with segments of data between successive changepoints. This approach is based on the use of recursions, and is related to work on product partition models. The computational complexity of the approach is quadratic in the number of observations, but an approximate version, which introduces negligible error, and whose computational cost is roughly linear in the number of observations, is also possible. Our approach can be useful, for example within an MCMC algorithm, even when the independence assumptions do not hold. We demonstrate our approach on coal-mining disaster data and on well-log data. Our method can cope with a range of models, and exact simulation from the posterior distribution is possible in a matter of minutes.     

Change points in nonparametric regresion functions

Estimators of location and size of jumps or discontinuities in a regression function and/or its derivatives are proposed. The estimators are based on the analysis of residuals obtained from the locally weighted least squares regression. The proposed estimators adapt to both fixed and random designs. The asymptotic properties of the estimators are investigated. The method is illustrated through simulation studies.     

Fair Valuation of Life Insurance Contracts Under a Two-Sided Jump Diffusion Model

In this article, we study the fair valuation of participating life insurance contract, which is one of the most common life insurance products, under the two-sided jump diffusion model with the consideration of default risk. The participating life insurance contracts considered here can be expressed as portfolios of options as shown by Grosen and Jøgrgensen (1997 Grosen , A. , Jøgrgensen , P. (1997). Valuation of early exercisable interest rate guarantees. J. Risk Ins. 64:481–503.[Crossref], [Web of Science ®] , [Google Scholar]). We can give the Laplace transforms for these options under the two-sided jump diffusion model, and then price these options by inverting Laplace transforms.     

Estimation of Jump Tails

We propose a new and flexible nonparametric framework for estimating the jump tails of Itô semimartingale processes. The approach is based on a relatively simple‐to‐implement set of estimating equations associated with the compensator for the jump measure, or its intensity, that only utilizes the weak assumption of regular variation in the jump tails, along with in‐fill asymptotic arguments for directly estimating the “large” jumps. The procedure assumes that the large‐sized jumps are identically distributed, but otherwise allows for very general dynamic dependencies in jump occurrences, and, importantly, does not restrict the behavior of the “small” jumps or the continuous part of the process and the temporal variation in the stochastic volatility. On implementing the new estimation procedure with actual high‐frequency data for the S&P 500 aggregate market portfolio, we find strong evidence for richer and more complex dynamic dependencies in the jump tails than hitherto entertained in the literature.