高斯过程机器学习在临河地铁车站基坑变形预测中的应用

为了更准确地对临河基坑开挖过程中出现的变形进行预测和风险预警,以天津地铁7号线王兰庄站出入口基坑临河施工为例,提出了一种基于改良高斯过程机器学习的临河基坑变形预测方法。首先,将施工过程收集的变形位移监测数据作为学习样本;其次,利用改良高斯过程回归算法对学习样本进行训练,并通过自适应不同的训练函数,获取较为合理的基坑变形代理模型;最后,通过代理模型预测基坑变形位移,并识别基坑风险,同时与传统高斯预测结果、有限元计算结果和实测值进行比较。结果表明：1）改良高斯过程回归方法较常规高斯过程的模拟效果更好,在样本点充足的条件下,可准确地根据基坑变形数据学习并预测后续基坑开挖的变形位移;2）相较于工程应用较多的有限元计算方法,采用改良高斯回归过程机器学习方法,可根据现场的实际监测数据对变形进行动态地学习、分析与预测。研究成果更贴近现场实际情况,具有较强的推广价值,可为基坑变形预测提供参考。     

LARGE DEVIATIONS IN MULTIFACTOR PORTFOLIO CREDIT RISK

The measurement of portfolio credit risk focuses on rare but significant large-loss events. This paper investigates rare event asymptotics for the loss distribution in the widely used Gaussian copula model of portfolio credit risk. We establish logarithmic limits for the tail of the loss distribution in two limiting regimes. The first limit examines the tail of the loss distribution at increasingly high loss thresholds; the second limiting regime is based on letting the individual loss probabilities decrease toward zero. Both limits are also based on letting the size of the portfolio increase. Our analysis reveals a qualitative distinction between the two cases: in the rare-default regime, the tail of the loss distribution decreases exponentially, but in the large-threshold regime the decay is consistent with a power law. This indicates that the dependence between defaults imposed by the Gaussian copula is qualitatively different for portfolios of high-quality and lower-quality credits.     

基于单因子利率期限结构模型的中国银行间短期利率行为的实证研究

文章采用高斯估计方法，使用中国银行间债券市场国债短期利率数据，对单因子连续时间利率期限结构模型进行了参数估计，实证结果显示我国银行间国债市场的短期利率具有均值恢复特性。和其它模型相比，BS模型在数据拟合方面表现较好。     

三类索赔额分布下的破产概率的模拟值及其R实现

破产概率的计算是精算破产理论的经典问题,对当前保险经营风险的度量有重要的理论意义和参考价值。在以往对破产概率的研究中,出于理论分析的方便,往往假设索赔额分布具有特殊的形式,而对更复杂的索赔额分布,求出理论上的解析解往往是不可行的,为此需要求解数值解。随机模拟是很重要的一种求数值解的方法。本文考虑三类索赔额分布:伽玛分布、对数正态分布、逆高斯分布,对每类分布,通过模拟不同参数下的索赔额,得到破产频数、首次破产对应的索赔次数的期望及标准差,并运用R软件对不同索赔额分布下的模拟结果进行比较分析。     

Continuous‐time mean–variance portfolio selection: A reinforcement learning framework

We approach the continuous‐time mean–variance portfolio selection with reinforcement learning (RL). The problem is to achieve the best trade‐off between exploration and exploitation, and is formulated as an entropy‐regularized, relaxed stochastic control problem. We prove that the optimal feedback policy for this problem must be Gaussian, with time‐decaying variance. We then prove a policy improvement theorem, based on which we devise an implementable RL algorithm. We find that our algorithm and its variant outperform both traditional and deep neural network based algorithms in our simulation and empirical studies.     

Marginal consistent dependence modelling using weak subordination for Brownian motions

We present an approach for modelling dependencies in exponential Lévy market models with arbitrary margins originated from time changed Brownian motions. Using weak subordination of Buchmann et al. [Bernoulli, 2017], we face a new layer of dependencies, superior to traditional approaches based on pathwise subordination, since weakly subordinated processes are not required to have independent components considering multivariate stochastic time changes. We apply a subordinator being able to incorporate any joint or idiosyncratic information arrivals. We emphasize multivariate variance gamma and normal inverse Gaussian processes and state explicit formulae for the Lévy characteristics. Using maximum likelihood, we estimate multivariate variance gamma models on various market data and show that these models are highly preferable to traditional approaches. Consistent values of basket-options under given marginal pricing models are achieved using the Esscher transform, generating a non-flat implied correlation surface.     

PRICING SWAPTIONS UNDER MULTIFACTOR GAUSSIAN HJM MODELS

Several approximations have been proposed in the literature for the pricing of European‐style swaptions under multifactor term structure models. However, none of them provides an estimate for the inherent approximation error. Until now, only the Edgeworth expansion technique of Collin‐Dufresne and Goldstein is able to characterize the order of the approximation error. Under a multifactor HJM Gaussian framework, this paper proposes a new approximation for European‐style swaptions, which is able to set bounds on the magnitude of the approximation error and is based on the conditioning approach initiated by Curran and Rogers and Shi. All the proposed pricing bounds will arise as a simple by‐product of the Nielsen and Sandmann setup, and will be shown to provide a better accuracy–efficiency trade‐off than all the approximations already proposed in the literature.     

铁路运输危险气体泄漏扩散模拟分析

针对铁路运输危险气体泄漏事故的特点,文章以高斯烟羽模型为基础,借助Matlab编程对不同条件下(不同风速、不同大气稳定条件和多泄漏源等)的铁路危险性气体扩散范围进行模拟分析,实现了危险性气体扩散的直观图形表示和伤害分区的划分,为指导铁路运输紧急救援提供一定的指导作用。     

数值保角变换的新算法

保角变换理论在流体力学等许多领域中有着广泛的应用。但计算保角变换是个很困难的问题,因此寻求一种有效方法计算保角变换在实际应用中具有很大意义。本论文提出了一种数值保角变换的新算法,在这个新算法中我们在改进高斯消去法的基础上利用模拟电荷法计算新的电荷点,进而构造高精度的近似保角变换函数,并且通过典型图形的数值实验检验了新算法的有效性。     

一种用于UWB系统的高斯脉冲发生器

提出了一种新型的用于超宽带系统的高斯脉冲发生器.该脉冲发生器采用阶跃恢复二极管,结构简单,且易于实现.电路中加入一个放大器,以便阻止反射波对阶跃恢复二极管的影响,较好地抑制了脉冲尾部的波动,并使用共面波导实现.该极窄高斯脉冲的脉宽仅为300ps,且有很好的对称性.